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How to Solve Equations (Change Sides, change sign)

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You now know that equations have to be balanced. That means that if you do something on one side of an equation, you have to do the same on the other side as well, to keep it from getting out of balance.

In order to isolate $x$ , you’ll want to add or subtract things to get rid of a term on one side of the equation. This is what you do:

Example 1

Subtracting on Both Sides

\begin{array}{l} x + 3 & = 5 \\ x + 3 - 3 & = 5 - 3 \\ x + 0 & = 2 \\ x & = 2 \end{array}

You want to remove the

3

on the left side (LS). If you subtract

3

from the LS, the

3

disappears. You have to subtract the

3

you subtracted from the left side from the right side (RS) as well. That means that the

3

showed up on the other side of the equal sign, but with the opposite sign!

Example 2

Adding on Both Sides

\begin{array}{l} x - 4 & = 9 \\ x - 4 + 4 & = 9 + 4 \\ x + 0 & = 13 \\ x & = 13 \end{array}

You want to remove the

- 4

on the LS. If you add

4

to the LS,

- 4

disappears. The

4

you added to the LS has to be added to the RS as well. That means that the

4

showed up on the other side of the equal sign, but with the opposite sign!

There is a simpler way than subtracting or adding on both sides. That method is called change sides, change sign.

Rule

The Change Sides, change sign Method

1.: Change sides of the term you want to remove so that it’s on the other side of the equal sign.
2.: Change the sign of the term you just moved.

Example 3

Positive Change Sides, change sign, to Negative

\begin{array}{l} x + 3 & = 5 \\ x & = 5 - 3 \\ x & = 2 \end{array}

+ 3

is changed to the RS of the equation. We change the sign so that

+ 3

becomes

- 3

Example 4

Negative Change Sides, Change Sign, to Positive

\begin{array}{l} x - 4 & = 9 \\ x & = 9 + 4 \\ x & = 13 \end{array}

- 4

is changed to the RS of the equation. We change its sign so that

- 4

becomes

+ 4

Why Can You Change Sides, change sign?

Why can you just change sides, change sign, as much as you like? Imagine that the scales are balanced. When you move a term over to the other scale, you would think it would get heavier, but because you change the sign at the same time, it’s like that same term was removed from or added to the other side of the scale as well!

Think About This

The change sides, change sign rule is a simplified way of completing the same action on both sides of the equal sign. Math is amazing that way—when you learn new rules, your life becomes easier!

Example 5

Solve the equation $x + 13 = 20$ .
$\begin{array}{l} x + 13 & = 20 \\ x & = 20 - 13 \\ x & = 7 \end{array}$

Example 6

Solve the equation $x - 41 = 69$ .

\begin{array}{l} x - 41 = 69 x & = 69 + 41 x & = 110Example 7 Solve the equation 2 x + 3 = 7 + x . \begin{array}{l} 2 x + 3 = 7 + x 2 x - x & = 7 - 3 x & = 4Example 8 Solve the equation 5 x - 11 = - 3 + 4 x . \begin{array}{l} 5 x - 11 = - 3 + 4 x 5 x - 4 x & = - 3 + 11 x & = 8Want to know more? Sign Up It's free!Previous entry What Is a Variable? Next entry How to Get Rid of the Number in Front of xGo backHome All Math Games Progress LeagueAbout Us About House of Math Employees Career Media Lectures Blog Contact support@houseofmath.com Booking of private tutoring +47 22 150 300 Address Bygdøy allé 23
            0262 Oslo
            Norway FAQ Links WeTakeAction Math Magic for Ukraine Tutoring Bootcamps Junior Math Pen & Paper exercises Encyclopedia Book a Tutor Language Norsk Українська Terms Privacy{"props":{"pageProps":{"campaign":false,"topic":{"path":"/encyclopedia/algebra/equations-and-inequalities/equations/linear-equations/how-to-solve-equations-change-sides-change-sign","h1":"How to Solve Equations (Change  Sides, change sign)","locale":"en","cssUrl":"/3e26151e-8cd9-466a-907f-43e1e928c4e8-en-0.css","taskReference":null,"sharedLanguageKey":null,"title":"How to Solve Equations (Change  Sides, change sign)","breadcrumbs":[{"path":"/encyclopedia","h1":"Encyclopedia","_key":"c0cf1a4b-5f7d-5390-9a52-e6ae2428b50c"},{"path":"/encyclopedia/algebra","h1":"Algebra","_key":"e9327e4b-42fe-571b-bcb9-83fdb63d5f21"},{"path":"/encyclopedia/algebra/equations-and-inequalities","h1":"Equations and Inequalities","_key":"100a0f18-3f76-5653-91ef-a410836c9583"},{"h1":"Equations","_key":"f99cf246-2b53-56b2-97b1-efb74d01f11e","path":"/encyclopedia/algebra/equations-and-inequalities/equations"},{"h1":"Linear Equations","_key":"ec8cfc0c-d586-5ca4-abda-92911b70eb65","path":"/encyclopedia/algebra/equations-and-inequalities/equations/linear-equations"},{"path":"/encyclopedia/algebra/equations-and-inequalities/equations/linear-equations/how-to-solve-equations-change-sides-change-sign","h1":"How to Solve Equations (Change  Sides, change sign)","_key":"312a45a2-bd74-5dc1-9955-225b3048f186"}],"isRootPath":false,"otherLocales":[],"key":"content/en/encyclopedia/02 Algebra/02 Equations and Inequalities/01 Equations/01 Linear Equations/104MoveSwitch.tex","image":null,"metaDescription":"Learn how to move numbers around in an equation while keeping it balanced by changing sides and changing signs. This is the key to solving equations.","language":"en","previewUrl":"https://images.houseofmath.com/eyJrZXkiOiJvdmVybGVhZi1hc3NldHMvcHJldmlldy8xMDRtb3Zlc3dpdGNoLnBuZyIsImJ1Y2tldCI6ImhvbS1mcm9udGVuZC1hc3NldHMiLCJ2ZXJzaW9uIjozfQ==","htmlContent":{"html":" \u003c/p\u003e      \u003cdiv class=\"tcolorbox foobootcamp\" id=\"tcolobox-1287\"\u003e     \u003cdiv class=\"tcolorbox-title\"\u003e                                                                                                                                                                                                                                          \u003cp class=\"indent\" \u003e     Video Crash Courses\u003c/p\u003e\u003c/div\u003e  \u003cdiv class=\"tcolorbox-content\"\u003e\u003cp class=\"noindent\" \u003eWant to watch animated videos and solve interactive exercises about moving numbers around in equations? \u003c/p\u003e\u003cp class=\"noindent\" \u003e\u003ca href=\"/bootcamp/algebra/equations/2/2/how\"\u003eClick here to try the Video Crash Course called “Linear Equations”!\u003c/a\u003e \u003c/p\u003e                                                                                                                     \u003c/div\u003e  \u003c/div\u003e                                                                                                                      \u003cp class=\"indent\" \u003e     You now know that equations have to be balanced. That means that if you do something on one side of an equation, you have to do the same on the other side as well, to keep it from getting out of balance. \u003c/p\u003e\u003cp class=\"indent\" \u003e     In order to isolate \u003cmath mathvariant=\"normal\"   xmlns=\"http://www.w3.org/1998/Math/MathML\"   display=\"inline\" \u003e\u003cmi  \u003ex\u003c/mi\u003e\u003c/math\u003e, you’ll want to add or subtract things to get rid of a term on one side of the equation. This is what you do: \u003c/p\u003e      \u003cdiv class=\"tcolorbox fooexample\" id=\"tcolobox-1288\"\u003e     \u003cdiv class=\"tcolorbox-title\"\u003e                                                                                                                                                                                                                                          \u003cp class=\"indent\" \u003e     Example 1\u003c/p\u003e\u003c/div\u003e  \u003cdiv class=\"tcolorbox-content\"\u003e\u003cp class=\"noindent\" \u003e\u003ch3 class=\"example-container-title\"\u003e \u003cspan  class=\"ec-lmbx-12x-x-172\"\u003eSubtracting\u003c/span\u003e \u003cspan  class=\"ec-lmbx-12x-x-172\"\u003eon\u003c/span\u003e \u003cspan  class=\"ec-lmbx-12x-x-172\"\u003eBoth\u003c/span\u003e \u003cspan  class=\"ec-lmbx-12x-x-172\"\u003eSides\u003c/span\u003e \u003c/h3\u003e \u003c/p\u003e\u003cp class=\"noindent\" \u003e \u003c/p\u003e\u003cmath mathvariant=\"normal\"   xmlns=\"http://www.w3.org/1998/Math/MathML\"   display=\"block\" \u003e\u003cmtable  columnalign=\"left\" class=\"align-star\"\u003e                                \u003cmtr\u003e\u003cmtd  columnalign=\"right\" class=\"align-odd\"\u003e\u003cmi  \u003ex\u003c/mi\u003e \u003cmo  class=\"MathClass-bin\"\u003e+\u003c/mo\u003e \u003cmn\u003e3\u003c/mn\u003e\u003c/mtd\u003e                                                   \u003cmtd  class=\"align-even\"\u003e \u003cmo  class=\"MathClass-rel\"\u003e=\u003c/mo\u003e \u003cmn\u003e5\u003c/mn\u003e\u003cmspace width=\"2em\"/\u003e\u003c/mtd\u003e                                                   \u003cmtd  columnalign=\"right\" class=\"align-label\"\u003e\u003c/mtd\u003e                                              \u003cmtd  class=\"align-label\"\u003e                                               \u003cmspace width=\"2em\"/\u003e\u003c/mtd\u003e\u003c/mtr\u003e\u003cmtr\u003e\u003cmtd  columnalign=\"right\" class=\"align-odd\"\u003e\u003cmi  \u003ex\u003c/mi\u003e \u003cmo  class=\"MathClass-bin\"\u003e+\u003c/mo\u003e \u003cmn\u003e3\u003c/mn\u003e\u003cmstyle mathcolor=\"#0056EB\"\u003e \u003cmo  class=\"MathClass-bin\"\u003e−\u003c/mo\u003e \u003cmn\u003e3\u003c/mn\u003e\u003c/mstyle\u003e\u003c/mtd\u003e                                              \u003cmtd  class=\"align-even\"\u003e \u003cmo  class=\"MathClass-rel\"\u003e=\u003c/mo\u003e \u003cmn\u003e5\u003c/mn\u003e\u003cmstyle mathcolor=\"#0056EB\"\u003e \u003cmo  class=\"MathClass-bin\"\u003e−\u003c/mo\u003e \u003cmn\u003e3\u003c/mn\u003e\u003c/mstyle\u003e\u003cmspace width=\"2em\"/\u003e\u003c/mtd\u003e                                              \u003cmtd  columnalign=\"right\" class=\"align-label\"\u003e\u003c/mtd\u003e                                              \u003cmtd  class=\"align-label\"\u003e                                               \u003cmspace width=\"2em\"/\u003e\u003c/mtd\u003e\u003c/mtr\u003e\u003cmtr\u003e\u003cmtd  columnalign=\"right\" class=\"align-odd\"\u003e\u003cmi  \u003ex\u003c/mi\u003e \u003cmo  class=\"MathClass-bin\"\u003e+\u003c/mo\u003e \u003cmn\u003e0\u003c/mn\u003e\u003c/mtd\u003e                                                   \u003cmtd  class=\"align-even\"\u003e \u003cmo  class=\"MathClass-rel\"\u003e=\u003c/mo\u003e \u003cmn\u003e2\u003c/mn\u003e\u003cmspace width=\"2em\"/\u003e\u003c/mtd\u003e                                                   \u003cmtd  columnalign=\"right\" class=\"align-label\"\u003e\u003c/mtd\u003e                                              \u003cmtd  class=\"align-label\"\u003e                                               \u003cmspace width=\"2em\"/\u003e\u003c/mtd\u003e\u003c/mtr\u003e\u003cmtr\u003e\u003cmtd  columnalign=\"right\" class=\"align-odd\"\u003e\u003cmi  \u003ex\u003c/mi\u003e\u003c/mtd\u003e                                            \u003cmtd  class=\"align-even\"\u003e \u003cmo  class=\"MathClass-rel\"\u003e=\u003c/mo\u003e \u003cmn\u003e2\u003c/mn\u003e\u003cmspace width=\"2em\"/\u003e\u003c/mtd\u003e                                                   \u003cmtd  columnalign=\"right\" class=\"align-label\"\u003e\u003c/mtd\u003e                                              \u003cmtd  class=\"align-label\"\u003e \u003cmspace width=\"2em\"/\u003e\u003c/mtd\u003e\u003c/mtr\u003e\u003c/mtable\u003e\u003c/math\u003e You want to remove the \u003cmath mathvariant=\"normal\"   xmlns=\"http://www.w3.org/1998/Math/MathML\"   display=\"inline\" \u003e\u003cmn\u003e3\u003c/mn\u003e\u003c/math\u003e on the left side (LS). If you subtract \u003cmath mathvariant=\"normal\"   xmlns=\"http://www.w3.org/1998/Math/MathML\"   display=\"inline\" \u003e\u003cmn\u003e3\u003c/mn\u003e\u003c/math\u003e from the LS, the \u003cmath mathvariant=\"normal\"   xmlns=\"http://www.w3.org/1998/Math/MathML\"   display=\"inline\" \u003e\u003cmn\u003e3\u003c/mn\u003e\u003c/math\u003e disappears. You have to subtract the \u003cmath mathvariant=\"normal\"   xmlns=\"http://www.w3.org/1998/Math/MathML\"   display=\"inline\" \u003e\u003cmn\u003e3\u003c/mn\u003e\u003c/math\u003e you subtracted from the left side from the right side (RS) as well. That means that the \u003cmath mathvariant=\"normal\"   xmlns=\"http://www.w3.org/1998/Math/MathML\"   display=\"inline\" \u003e\u003cmn\u003e3\u003c/mn\u003e\u003c/math\u003e showed up on the other side of the equal sign, but with the opposite sign!                    \u003c/div\u003e  \u003c/div\u003e                                                                                                                           \u003cdiv class=\"tcolorbox fooexample\" id=\"tcolobox-1289\"\u003e     \u003cdiv class=\"tcolorbox-title\"\u003e                                                                                                                                                                                                                                          \u003cp class=\"indent\" \u003e     Example 2\u003c/p\u003e\u003c/div\u003e  \u003cdiv class=\"tcolorbox-content\"\u003e\u003cp class=\"noindent\" \u003e\u003ch3 class=\"example-container-title\"\u003e \u003cspan  class=\"ec-lmbx-12x-x-172\"\u003eAdding\u003c/span\u003e \u003cspan  class=\"ec-lmbx-12x-x-172\"\u003eon\u003c/span\u003e \u003cspan  class=\"ec-lmbx-12x-x-172\"\u003eBoth\u003c/span\u003e \u003cspan  class=\"ec-lmbx-12x-x-172\"\u003eSides\u003c/span\u003e \u003c/h3\u003e \u003c/p\u003e\u003cp class=\"noindent\" \u003e \u003c/p\u003e\u003cmath mathvariant=\"normal\"   xmlns=\"http://www.w3.org/1998/Math/MathML\"   display=\"block\" \u003e\u003cmtable  columnalign=\"left\" class=\"align-star\"\u003e                                \u003cmtr\u003e\u003cmtd  columnalign=\"right\" class=\"align-odd\"\u003e\u003cmi  \u003ex\u003c/mi\u003e \u003cmo  class=\"MathClass-bin\"\u003e−\u003c/mo\u003e \u003cmn\u003e4\u003c/mn\u003e\u003c/mtd\u003e                                                   \u003cmtd  class=\"align-even\"\u003e \u003cmo  class=\"MathClass-rel\"\u003e=\u003c/mo\u003e \u003cmn\u003e9\u003c/mn\u003e\u003cmspace width=\"2em\"/\u003e\u003c/mtd\u003e                                                   \u003cmtd  columnalign=\"right\" class=\"align-label\"\u003e\u003c/mtd\u003e                                              \u003cmtd  class=\"align-label\"\u003e                                               \u003cmspace width=\"2em\"/\u003e\u003c/mtd\u003e\u003c/mtr\u003e\u003cmtr\u003e\u003cmtd  columnalign=\"right\" class=\"align-odd\"\u003e\u003cmi  \u003ex\u003c/mi\u003e \u003cmo  class=\"MathClass-bin\"\u003e−\u003c/mo\u003e \u003cmn\u003e4\u003c/mn\u003e\u003cmstyle mathcolor=\"#0056EB\"\u003e \u003cmo  class=\"MathClass-bin\"\u003e+\u003c/mo\u003e \u003cmn\u003e4\u003c/mn\u003e\u003c/mstyle\u003e\u003c/mtd\u003e                                              \u003cmtd  class=\"align-even\"\u003e \u003cmo  class=\"MathClass-rel\"\u003e=\u003c/mo\u003e \u003cmn\u003e9\u003c/mn\u003e\u003cmstyle mathcolor=\"#0056EB\"\u003e \u003cmo  class=\"MathClass-bin\"\u003e+\u003c/mo\u003e \u003cmn\u003e4\u003c/mn\u003e\u003c/mstyle\u003e\u003cmspace width=\"2em\"/\u003e\u003c/mtd\u003e                                              \u003cmtd  columnalign=\"right\" class=\"align-label\"\u003e\u003c/mtd\u003e                                              \u003cmtd  class=\"align-label\"\u003e                                               \u003cmspace width=\"2em\"/\u003e\u003c/mtd\u003e\u003c/mtr\u003e\u003cmtr\u003e\u003cmtd  columnalign=\"right\" class=\"align-odd\"\u003e\u003cmi  \u003ex\u003c/mi\u003e \u003cmo  class=\"MathClass-bin\"\u003e+\u003c/mo\u003e \u003cmn\u003e0\u003c/mn\u003e\u003c/mtd\u003e                                                   \u003cmtd  class=\"align-even\"\u003e \u003cmo  class=\"MathClass-rel\"\u003e=\u003c/mo\u003e \u003cmn\u003e1\u003c/mn\u003e\u003cmn\u003e3\u003c/mn\u003e\u003cmspace width=\"2em\"/\u003e\u003c/mtd\u003e                                                  \u003cmtd  columnalign=\"right\" class=\"align-label\"\u003e\u003c/mtd\u003e                                              \u003cmtd  class=\"align-label\"\u003e                                               \u003cmspace width=\"2em\"/\u003e\u003c/mtd\u003e\u003c/mtr\u003e\u003cmtr\u003e\u003cmtd  columnalign=\"right\" class=\"align-odd\"\u003e\u003cmi  \u003ex\u003c/mi\u003e\u003c/mtd\u003e                                            \u003cmtd  class=\"align-even\"\u003e \u003cmo  class=\"MathClass-rel\"\u003e=\u003c/mo\u003e \u003cmn\u003e1\u003c/mn\u003e\u003cmn\u003e3\u003c/mn\u003e\u003cmspace width=\"2em\"/\u003e\u003c/mtd\u003e                                                  \u003cmtd  columnalign=\"right\" class=\"align-label\"\u003e\u003c/mtd\u003e                                              \u003cmtd  class=\"align-label\"\u003e \u003cmspace width=\"2em\"/\u003e\u003c/mtd\u003e\u003c/mtr\u003e\u003c/mtable\u003e\u003c/math\u003e You want to remove the \u003cmath mathvariant=\"normal\"   xmlns=\"http://www.w3.org/1998/Math/MathML\"   display=\"inline\" \u003e \u003cmo  class=\"MathClass-bin\"\u003e−\u003c/mo\u003e \u003cmn\u003e4\u003c/mn\u003e\u003c/math\u003e on the LS. If you add \u003cmath mathvariant=\"normal\"   xmlns=\"http://www.w3.org/1998/Math/MathML\"   display=\"inline\" \u003e\u003cmn\u003e4\u003c/mn\u003e\u003c/math\u003e to the LS, \u003cmath mathvariant=\"normal\"   xmlns=\"http://www.w3.org/1998/Math/MathML\"   display=\"inline\" \u003e \u003cmo  class=\"MathClass-bin\"\u003e−\u003c/mo\u003e \u003cmn\u003e4\u003c/mn\u003e\u003c/math\u003e disappears. The \u003cmath mathvariant=\"normal\"   xmlns=\"http://www.w3.org/1998/Math/MathML\"   display=\"inline\" \u003e\u003cmn\u003e4\u003c/mn\u003e\u003c/math\u003e you added to the LS has to be added to the RS as well. That means that the \u003cmath mathvariant=\"normal\"   xmlns=\"http://www.w3.org/1998/Math/MathML\"   display=\"inline\" \u003e\u003cmn\u003e4\u003c/mn\u003e\u003c/math\u003e showed up on the other side of the equal sign, but with the opposite sign!                    \u003c/div\u003e  \u003c/div\u003e                                                                                                                      \u003cp class=\"indent\" \u003e     There is a simpler way than subtracting or adding on both sides. That method is called \u003cspan  class=\"ec-lmri-12x-x-144\"\u003echange sides, change sign\u003c/span type=\"punct\"\u003e. \u003c/p\u003e      \u003cdiv class=\"tcolorbox foorule\" id=\"tcolobox-1290\"\u003e     \u003cdiv class=\"tcolorbox-title\"\u003e                                                                                                                                                                                                                                          \u003cp class=\"indent\" \u003e     Rule\u003c/p\u003e\u003c/div\u003e  \u003cdiv class=\"tcolorbox-content\"\u003e\u003cp class=\"noindent\" \u003e\u003ch3 class=\"rule-container-title\"\u003e \u003cspan  class=\"ec-lmbx-12x-x-172\"\u003eThe\u003c/span\u003e \u003cspan  class=\"ec-lmbx-12x-x-172\"\u003eChange\u003c/span\u003e \u003cspan  class=\"ec-lmbx-12x-x-172\"\u003eSides,\u003c/span\u003e \u003cspan  class=\"ec-lmbx-12x-x-172\"\u003echange\u003c/span\u003e \u003cspan  class=\"ec-lmbx-12x-x-172\"\u003esign\u003c/span\u003e \u003cspan  class=\"ec-lmbx-12x-x-172\"\u003eMethod\u003c/span\u003e \u003c/h3\u003e \u003c/p\u003e\u003cp class=\"noindent\" \u003e      \u003c/p\u003e\u003cdl class=\"enumerate-enumitem\"\u003e\u003cdt class=\"enumerate-enumitem\"\u003e    1.  \u003c/dt\u003e\u003cdd  class=\"enumerate-enumitem\"\u003e         Change         sides         of         the         term         you         want         to         remove         so         that         it’s         on         the         other         side         of         the         equal         sign.         \u003c/dd\u003e\u003cdt class=\"enumerate-enumitem\"\u003e     2.  \u003c/dt\u003e\u003cdd  class=\"enumerate-enumitem\"\u003e         Change         the         sign         of         the         term         you         just         moved.         \u003c/dd\u003e\u003c/dl\u003e                                                                                                                      \u003c/div\u003e  \u003c/div\u003e                                                                                                                           \u003cdiv class=\"tcolorbox fooexample\" id=\"tcolobox-1291\"\u003e     \u003cdiv class=\"tcolorbox-title\"\u003e                                                                                                                                                                                                                                          \u003cp class=\"indent\" \u003e     Example 3\u003c/p\u003e\u003c/div\u003e  \u003cdiv class=\"tcolorbox-content\"\u003e\u003cp class=\"noindent\" \u003e\u003ch3 class=\"example-container-title\"\u003e \u003cspan  class=\"ec-lmbx-12x-x-172\"\u003ePositive\u003c/span\u003e \u003cspan  class=\"ec-lmbx-12x-x-172\"\u003eChange\u003c/span\u003e \u003cspan  class=\"ec-lmbx-12x-x-172\"\u003eSides,\u003c/span\u003e \u003cspan  class=\"ec-lmbx-12x-x-172\"\u003echange\u003c/span\u003e \u003cspan  class=\"ec-lmbx-12x-x-172\"\u003esign,\u003c/span\u003e \u003cspan  class=\"ec-lmbx-12x-x-172\"\u003eto\u003c/span\u003e \u003cspan  class=\"ec-lmbx-12x-x-172\"\u003eNegative\u003c/span\u003e \u003c/h3\u003e \u003c/p\u003e\u003cp class=\"noindent\" \u003e \u003c/p\u003e\u003cmath mathvariant=\"normal\"   xmlns=\"http://www.w3.org/1998/Math/MathML\"   display=\"block\" \u003e\u003cmtable  columnalign=\"left\" class=\"align-star\"\u003e                                  \u003cmtr\u003e\u003cmtd  columnalign=\"right\" class=\"align-odd\"\u003e\u003cmi  \u003ex\u003c/mi\u003e \u003cmo  class=\"MathClass-bin\"\u003e+\u003c/mo\u003e \u003cmn\u003e3\u003c/mn\u003e\u003c/mtd\u003e                                                \u003cmtd  class=\"align-even\"\u003e \u003cmo  class=\"MathClass-rel\"\u003e=\u003c/mo\u003e \u003cmn\u003e5\u003c/mn\u003e\u003cmspace width=\"2em\"/\u003e\u003c/mtd\u003e                                                      \u003cmtd  columnalign=\"right\" class=\"align-label\"\u003e\u003c/mtd\u003e                                                \u003cmtd  class=\"align-label\"\u003e                                                 \u003cmspace width=\"2em\"/\u003e\u003c/mtd\u003e\u003c/mtr\u003e\u003cmtr\u003e\u003cmtd  columnalign=\"right\" class=\"align-odd\"\u003e\u003cmi  \u003ex\u003c/mi\u003e\u003c/mtd\u003e                                          \u003cmtd  class=\"align-even\"\u003e \u003cmo  class=\"MathClass-rel\"\u003e=\u003c/mo\u003e \u003cmn\u003e5\u003c/mn\u003e\u003cmstyle mathcolor=\"#0056EB\"\u003e \u003cmo  class=\"MathClass-bin\"\u003e−\u003c/mo\u003e \u003cmn\u003e3\u003c/mn\u003e\u003c/mstyle\u003e\u003cmspace width=\"2em\"/\u003e\u003c/mtd\u003e                                                \u003cmtd  columnalign=\"right\" class=\"align-label\"\u003e\u003c/mtd\u003e                                                \u003cmtd  class=\"align-label\"\u003e                                                 \u003cmspace width=\"2em\"/\u003e\u003c/mtd\u003e\u003c/mtr\u003e\u003cmtr\u003e\u003cmtd  columnalign=\"right\" class=\"align-odd\"\u003e\u003cmi  \u003ex\u003c/mi\u003e\u003c/mtd\u003e                                          \u003cmtd  class=\"align-even\"\u003e \u003cmo  class=\"MathClass-rel\"\u003e=\u003c/mo\u003e \u003cmn\u003e2\u003c/mn\u003e\u003cmspace width=\"2em\"/\u003e\u003c/mtd\u003e                                                      \u003cmtd  columnalign=\"right\" class=\"align-label\"\u003e\u003c/mtd\u003e                                                \u003cmtd  class=\"align-label\"\u003e \u003cmspace width=\"2em\"/\u003e\u003c/mtd\u003e\u003c/mtr\u003e\u003c/mtable\u003e\u003c/math\u003e \u003cmath mathvariant=\"normal\"   xmlns=\"http://www.w3.org/1998/Math/MathML\"   display=\"inline\" \u003e \u003cmo  class=\"MathClass-bin\"\u003e+\u003c/mo\u003e \u003cmn\u003e3\u003c/mn\u003e\u003c/math\u003e is \u003cspan  class=\"ec-lmri-12x-x-144\"\u003echanged to the RS \u003c/span\u003eof the equation. We \u003cspan  class=\"ec-lmri-12x-x-144\"\u003echange the sign \u003c/span\u003eso that \u003cmath mathvariant=\"normal\"   xmlns=\"http://www.w3.org/1998/Math/MathML\"   display=\"inline\" \u003e \u003cmo  class=\"MathClass-bin\"\u003e+\u003c/mo\u003e \u003cmn\u003e3\u003c/mn\u003e\u003c/math\u003e becomes \u003cmath mathvariant=\"normal\"   xmlns=\"http://www.w3.org/1998/Math/MathML\"   display=\"inline\" \u003e \u003cmo  class=\"MathClass-bin\"\u003e−\u003c/mo\u003e \u003cmn\u003e3\u003c/mn\u003e\u003c/math type=\"punct\"\u003e.   \u003c/div\u003e  \u003c/div\u003e                                                                                                                           \u003cdiv class=\"tcolorbox fooexample\" id=\"tcolobox-1292\"\u003e     \u003cdiv class=\"tcolorbox-title\"\u003e                                                                                                                                                                                                                                          \u003cp class=\"indent\" \u003e     Example 4\u003c/p\u003e\u003c/div\u003e  \u003cdiv class=\"tcolorbox-content\"\u003e\u003cp class=\"noindent\" \u003e\u003ch3 class=\"example-container-title\"\u003e \u003cspan  class=\"ec-lmbx-12x-x-172\"\u003eNegative\u003c/span\u003e \u003cspan  class=\"ec-lmbx-12x-x-172\"\u003eChange\u003c/span\u003e \u003cspan  class=\"ec-lmbx-12x-x-172\"\u003eSides,\u003c/span\u003e \u003cspan  class=\"ec-lmbx-12x-x-172\"\u003eChange\u003c/span\u003e \u003cspan  class=\"ec-lmbx-12x-x-172\"\u003eSign,\u003c/span\u003e \u003cspan  class=\"ec-lmbx-12x-x-172\"\u003eto\u003c/span\u003e \u003cspan  class=\"ec-lmbx-12x-x-172\"\u003ePositive\u003c/span\u003e \u003c/h3\u003e \u003c/p\u003e\u003cp class=\"noindent\" \u003e \u003c/p\u003e\u003cmath mathvariant=\"normal\"   xmlns=\"http://www.w3.org/1998/Math/MathML\"   display=\"block\" \u003e\u003cmtable  columnalign=\"left\" class=\"align-star\"\u003e                                  \u003cmtr\u003e\u003cmtd  columnalign=\"right\" class=\"align-odd\"\u003e\u003cmi  \u003ex\u003c/mi\u003e \u003cmo  class=\"MathClass-bin\"\u003e−\u003c/mo\u003e \u003cmn\u003e4\u003c/mn\u003e\u003c/mtd\u003e                                                \u003cmtd  class=\"align-even\"\u003e \u003cmo  class=\"MathClass-rel\"\u003e=\u003c/mo\u003e \u003cmn\u003e9\u003c/mn\u003e\u003cmspace width=\"2em\"/\u003e\u003c/mtd\u003e                                                      \u003cmtd  columnalign=\"right\" class=\"align-label\"\u003e\u003c/mtd\u003e                                                \u003cmtd  class=\"align-label\"\u003e                                                 \u003cmspace width=\"2em\"/\u003e\u003c/mtd\u003e\u003c/mtr\u003e\u003cmtr\u003e\u003cmtd  columnalign=\"right\" class=\"align-odd\"\u003e\u003cmi  \u003ex\u003c/mi\u003e\u003c/mtd\u003e                                          \u003cmtd  class=\"align-even\"\u003e \u003cmo  class=\"MathClass-rel\"\u003e=\u003c/mo\u003e \u003cmn\u003e9\u003c/mn\u003e\u003cmstyle mathcolor=\"#0056EB\"\u003e \u003cmo  class=\"MathClass-bin\"\u003e+\u003c/mo\u003e \u003cmn\u003e4\u003c/mn\u003e\u003c/mstyle\u003e\u003cmspace width=\"2em\"/\u003e\u003c/mtd\u003e                                                \u003cmtd  columnalign=\"right\" class=\"align-label\"\u003e\u003c/mtd\u003e                                                \u003cmtd  class=\"align-label\"\u003e                                                 \u003cmspace width=\"2em\"/\u003e\u003c/mtd\u003e\u003c/mtr\u003e\u003cmtr\u003e\u003cmtd  columnalign=\"right\" class=\"align-odd\"\u003e\u003cmi  \u003ex\u003c/mi\u003e\u003c/mtd\u003e                                          \u003cmtd  class=\"align-even\"\u003e \u003cmo  class=\"MathClass-rel\"\u003e=\u003c/mo\u003e \u003cmn\u003e1\u003c/mn\u003e\u003cmn\u003e3\u003c/mn\u003e\u003cmspace width=\"2em\"/\u003e\u003c/mtd\u003e                                                    \u003cmtd  columnalign=\"right\" class=\"align-label\"\u003e\u003c/mtd\u003e                                                \u003cmtd  class=\"align-label\"\u003e \u003cmspace width=\"2em\"/\u003e\u003c/mtd\u003e\u003c/mtr\u003e\u003c/mtable\u003e\u003c/math\u003e \u003cmath mathvariant=\"normal\"   xmlns=\"http://www.w3.org/1998/Math/MathML\"   display=\"inline\" \u003e \u003cmo  class=\"MathClass-bin\"\u003e−\u003c/mo\u003e \u003cmn\u003e4\u003c/mn\u003e\u003c/math\u003e is \u003cspan  class=\"ec-lmri-12x-x-144\"\u003echanged to the RS \u003c/span\u003eof the equation. We \u003cspan  class=\"ec-lmri-12x-x-144\"\u003echange its sign \u003c/span\u003eso that \u003cmath mathvariant=\"normal\"   xmlns=\"http://www.w3.org/1998/Math/MathML\"   display=\"inline\" \u003e \u003cmo  class=\"MathClass-bin\"\u003e−\u003c/mo\u003e \u003cmn\u003e4\u003c/mn\u003e\u003c/math\u003e becomes \u003cmath mathvariant=\"normal\"   xmlns=\"http://www.w3.org/1998/Math/MathML\"   display=\"inline\" \u003e \u003cmo  class=\"MathClass-bin\"\u003e+\u003c/mo\u003e \u003cmn\u003e4\u003c/mn\u003e\u003c/math type=\"punct\"\u003e.   \u003c/div\u003e  \u003c/div\u003e                                                                                                                      \u003cp class=\"noindent\" \u003e \u003c/p\u003e \u003cp class=\"indent\" \u003e     \u003ch2 class=\"section-title\"\u003e \u003ca   id=\"x1-517000\"\u003e\u003c/a\u003eWhy Can You Change Sides, change sign?\u003c/h2\u003e \u003c/p\u003e\u003cp class=\"indent\" \u003e     Why can you just change sides, change sign, as much as you like? Imagine that the scales are balanced. When you move a term over to the other scale, you would think it would get heavier, but because you change the sign at the same time, it’s like that same term was removed from or added to the other side of the scale as well! \u003c/p\u003e      \u003cdiv class=\"tcolorbox foothink\" id=\"tcolobox-1293\"\u003e     \u003cdiv class=\"tcolorbox-title\"\u003e                                                                                                                                                                                                                                          \u003cp class=\"indent\" \u003e     Think About This\u003c/p\u003e\u003c/div\u003e  \u003cdiv class=\"tcolorbox-content\"\u003e\u003cp class=\"noindent\" \u003eThe change sides, change sign rule is a simplified way of completing the same action on both sides of the equal sign. \u003c/p\u003e\u003cp class=\"noindent\" \u003eMath is amazing that way—when you learn new rules, your life becomes easier! \u003c/p\u003e                                                                                                                     \u003c/div\u003e  \u003c/div\u003e                                                                                                                           \u003cdiv class=\"tcolorbox fooqaexample\" id=\"tcolobox-1294\"\u003e     \u003cdiv class=\"tcolorbox-title\"\u003e \u003cp class=\"indent\" \u003e     Example 5\u003c/p\u003e\u003c/div\u003e  \u003cdiv class=\"tcolorbox-content\"\u003e\u003cp class=\"noindent\" \u003e\u003cb\u003e\u003cspan  class=\"ec-lmbx-12x-x-144\"\u003eSolve the equation \u003c/span\u003e\u003cmath mathvariant=\"normal\"   xmlns=\"http://www.w3.org/1998/Math/MathML\"   display=\"inline\" \u003e\u003cmstyle mathvariant=\"bold-italic\"\u003e\u003cmstyle mathvariant=\"bold\"\u003e\u003cmi  \u003ex\u003c/mi\u003e \u003cmo  class=\"MathClass-bin\"\u003e+\u003c/mo\u003e \u003cmn\u003e1\u003c/mn\u003e\u003cmn\u003e3\u003c/mn\u003e \u003cmo  class=\"MathClass-rel\"\u003e=\u003c/mo\u003e \u003cmn\u003e2\u003c/mn\u003e\u003cmn\u003e0\u003c/mn\u003e\u003c/mstyle\u003e\u003c/mstyle\u003e\u003c/math\u003e\u003cspan  class=\"ec-lmbx-12x-x-144\" type=\"punct\"\u003e.\u003c/span\u003e \u003c/p\u003e\u003cmath mathvariant=\"normal\"   xmlns=\"http://www.w3.org/1998/Math/MathML\"   display=\"block\" \u003e\u003cmtable  columnalign=\"left\" class=\"align-star\"\u003e                                    \u003cmtr\u003e\u003cmtd  columnalign=\"right\" class=\"align-odd\"\u003e\u003cmi  \u003ex\u003c/mi\u003e \u003cmo  class=\"MathClass-bin\"\u003e+\u003c/mo\u003e \u003cmn\u003e1\u003c/mn\u003e\u003cmn\u003e3\u003c/mn\u003e\u003c/mtd\u003e                                   \u003cmtd  class=\"align-even\"\u003e \u003cmo  class=\"MathClass-rel\"\u003e=\u003c/mo\u003e \u003cmn\u003e2\u003c/mn\u003e\u003cmn\u003e0\u003c/mn\u003e\u003cmspace width=\"2em\"/\u003e\u003c/mtd\u003e                                          \u003cmtd  columnalign=\"right\" class=\"align-label\"\u003e\u003c/mtd\u003e                                   \u003cmtd  class=\"align-label\"\u003e                                    \u003cmspace width=\"2em\"/\u003e\u003c/mtd\u003e\u003c/mtr\u003e\u003cmtr\u003e\u003cmtd  columnalign=\"right\" class=\"align-odd\"\u003e\u003cmi  \u003ex\u003c/mi\u003e\u003c/mtd\u003e                                   \u003cmtd  class=\"align-even\"\u003e \u003cmo  class=\"MathClass-rel\"\u003e=\u003c/mo\u003e \u003cmn\u003e2\u003c/mn\u003e\u003cmn\u003e0\u003c/mn\u003e\u003cmstyle mathcolor=\"#0056EB\"\u003e \u003cmo  class=\"MathClass-bin\"\u003e−\u003c/mo\u003e \u003cmn\u003e1\u003c/mn\u003e\u003cmn\u003e3\u003c/mn\u003e\u003c/mstyle\u003e\u003cmspace width=\"2em\"/\u003e\u003c/mtd\u003e                                   \u003cmtd  columnalign=\"right\" class=\"align-label\"\u003e\u003c/mtd\u003e                                   \u003cmtd  class=\"align-label\"\u003e                                    \u003cmspace width=\"2em\"/\u003e\u003c/mtd\u003e\u003c/mtr\u003e\u003cmtr\u003e\u003cmtd  columnalign=\"right\" class=\"align-odd\"\u003e\u003cmi  \u003ex\u003c/mi\u003e\u003c/mtd\u003e                                   \u003cmtd  class=\"align-even\"\u003e \u003cmo  class=\"MathClass-rel\"\u003e=\u003c/mo\u003e \u003cmn\u003e7\u003c/mn\u003e\u003cmspace width=\"2em\"/\u003e\u003c/mtd\u003e                                            \u003cmtd  columnalign=\"right\" class=\"align-label\"\u003e\u003c/mtd\u003e                                   \u003cmtd  class=\"align-label\"\u003e \u003cmspace width=\"2em\"/\u003e\u003c/mtd\u003e\u003c/mtr\u003e\u003c/mtable\u003e\u003c/math\u003e \u003c/b\u003e                                                                                               \u003c/div\u003e  \u003c/div\u003e      \u003cdiv class=\"tcolorbox fooqaexample\" id=\"tcolobox-1295\"\u003e     \u003cdiv class=\"tcolorbox-title\"\u003e                                                                                                                                                                                                                                          \u003cp class=\"indent\" \u003e     Example 6\u003c/p\u003e\u003c/div\u003e  \u003cdiv class=\"tcolorbox-content\"\u003e\u003cp class=\"noindent\" \u003e\u003cb\u003e\u003cspan  class=\"ec-lmbx-12x-x-144\"\u003eSolve the equation \u003c/span\u003e\u003cmath mathvariant=\"normal\"   xmlns=\"http://www.w3.org/1998/Math/MathML\"   display=\"inline\" \u003e\u003cmstyle mathvariant=\"bold-italic\"\u003e\u003cmstyle mathvariant=\"bold\"\u003e\u003cmi  \u003ex\u003c/mi\u003e \u003cmo  class=\"MathClass-bin\"\u003e−\u003c/mo\u003e \u003cmn\u003e4\u003c/mn\u003e\u003cmn\u003e1\u003c/mn\u003e \u003cmo  class=\"MathClass-rel\"\u003e=\u003c/mo\u003e \u003cmn\u003e6\u003c/mn\u003e\u003cmn\u003e9\u003c/mn\u003e\u003c/mstyle\u003e\u003c/mstyle\u003e\u003c/math\u003e\u003cspan  class=\"ec-lmbx-12x-x-144\" type=\"punct\"\u003e.\u003c/span\u003e \u003c/p\u003e\u003cmath mathvariant=\"normal\"   xmlns=\"http://www.w3.org/1998/Math/MathML\"   display=\"block\" \u003e\u003cmtable  columnalign=\"left\" class=\"align-star\"\u003e                                    \u003cmtr\u003e\u003cmtd  columnalign=\"right\" class=\"align-odd\"\u003e\u003cmi  \u003ex\u003c/mi\u003e \u003cmo  class=\"MathClass-bin\"\u003e−\u003c/mo\u003e \u003cmn\u003e4\u003c/mn\u003e\u003cmn\u003e1\u003c/mn\u003e\u003c/mtd\u003e                                   \u003cmtd  class=\"align-even\"\u003e \u003cmo  class=\"MathClass-rel\"\u003e=\u003c/mo\u003e \u003cmn\u003e6\u003c/mn\u003e\u003cmn\u003e9\u003c/mn\u003e\u003cmspace width=\"2em\"/\u003e\u003c/mtd\u003e                                          \u003cmtd  columnalign=\"right\" class=\"align-label\"\u003e\u003c/mtd\u003e                                   \u003cmtd  class=\"align-label\"\u003e                                    \u003cmspace width=\"2em\"/\u003e\u003c/mtd\u003e\u003c/mtr\u003e\u003cmtr\u003e\u003cmtd  columnalign=\"right\" class=\"align-odd\"\u003e\u003cmi  \u003ex\u003c/mi\u003e\u003c/mtd\u003e                                   \u003cmtd  class=\"align-even\"\u003e \u003cmo  class=\"MathClass-rel\"\u003e=\u003c/mo\u003e \u003cmn\u003e6\u003c/mn\u003e\u003cmn\u003e9\u003c/mn\u003e\u003cmstyle mathcolor=\"#0056EB\"\u003e \u003cmo  class=\"MathClass-bin\"\u003e+\u003c/mo\u003e \u003cmn\u003e4\u003c/mn\u003e\u003cmn\u003e1\u003c/mn\u003e\u003c/mstyle\u003e\u003cmspace width=\"2em\"/\u003e\u003c/mtd\u003e                                   \u003cmtd  columnalign=\"right\" class=\"align-label\"\u003e\u003c/mtd\u003e                                   \u003cmtd  class=\"align-label\"\u003e                                    \u003cmspace width=\"2em\"/\u003e\u003c/mtd\u003e\u003c/mtr\u003e\u003cmtr\u003e\u003cmtd  columnalign=\"right\" class=\"align-odd\"\u003e\u003cmi  \u003ex\u003c/mi\u003e\u003c/mtd\u003e                                   \u003cmtd  class=\"align-even\"\u003e \u003cmo  class=\"MathClass-rel\"\u003e=\u003c/mo\u003e \u003cmn\u003e1\u003c/mn\u003e\u003cmn\u003e1\u003c/mn\u003e\u003cmn\u003e0\u003c/mn\u003e\u003cmspace width=\"2em\"/\u003e\u003c/mtd\u003e                                         \u003cmtd  columnalign=\"right\" class=\"align-label\"\u003e\u003c/mtd\u003e                                   \u003cmtd  class=\"align-label\"\u003e \u003cmspace width=\"2em\"/\u003e\u003c/mtd\u003e\u003c/mtr\u003e\u003c/mtable\u003e\u003c/math\u003e \u003c/b\u003e                                                                                               \u003c/div\u003e  \u003c/div\u003e      \u003cdiv class=\"tcolorbox fooqaexample\" id=\"tcolobox-1296\"\u003e     \u003cdiv class=\"tcolorbox-title\"\u003e                                                                                                                                                                                                                                          \u003cp class=\"indent\" \u003e     Example 7\u003c/p\u003e\u003c/div\u003e  \u003cdiv class=\"tcolorbox-content\"\u003e\u003cp class=\"noindent\" \u003e\u003cb\u003e\u003cspan  class=\"ec-lmbx-12x-x-144\"\u003eSolve the equation \u003c/span\u003e\u003cmath mathvariant=\"normal\"   xmlns=\"http://www.w3.org/1998/Math/MathML\"   display=\"inline\" \u003e\u003cmstyle mathvariant=\"bold-italic\"\u003e\u003cmstyle mathvariant=\"bold\"\u003e\u003cmn\u003e2\u003c/mn\u003e\u003cmi  \u003ex\u003c/mi\u003e \u003cmo  class=\"MathClass-bin\"\u003e+\u003c/mo\u003e \u003cmn\u003e3\u003c/mn\u003e \u003cmo  class=\"MathClass-rel\"\u003e=\u003c/mo\u003e \u003cmn\u003e7\u003c/mn\u003e \u003cmo  class=\"MathClass-bin\"\u003e+\u003c/mo\u003e \u003cmi  \u003ex\u003c/mi\u003e\u003c/mstyle\u003e\u003c/mstyle\u003e\u003c/math\u003e\u003cspan  class=\"ec-lmbx-12x-x-144\" type=\"punct\"\u003e.\u003c/span\u003e \u003c/p\u003e\u003cmath mathvariant=\"normal\"   xmlns=\"http://www.w3.org/1998/Math/MathML\"   display=\"block\" \u003e\u003cmtable  columnalign=\"left\" class=\"align-star\"\u003e                                      \u003cmtr\u003e\u003cmtd  columnalign=\"right\" class=\"align-odd\"\u003e\u003cmn\u003e2\u003c/mn\u003e\u003cmi  \u003ex\u003c/mi\u003e \u003cmo  class=\"MathClass-bin\"\u003e+\u003c/mo\u003e \u003cmn\u003e3\u003c/mn\u003e\u003c/mtd\u003e                                     \u003cmtd  class=\"align-even\"\u003e \u003cmo  class=\"MathClass-rel\"\u003e=\u003c/mo\u003e \u003cmn\u003e7\u003c/mn\u003e \u003cmo  class=\"MathClass-bin\"\u003e+\u003c/mo\u003e \u003cmi  \u003ex\u003c/mi\u003e\u003cmspace width=\"2em\"/\u003e\u003c/mtd\u003e                              \u003cmtd  columnalign=\"right\" class=\"align-label\"\u003e\u003c/mtd\u003e                              \u003cmtd  class=\"align-label\"\u003e                               \u003cmspace width=\"2em\"/\u003e\u003c/mtd\u003e\u003c/mtr\u003e\u003cmtr\u003e\u003cmtd  columnalign=\"right\" class=\"align-odd\"\u003e\u003cmn\u003e2\u003c/mn\u003e\u003cmi  \u003ex\u003c/mi\u003e\u003cmstyle mathcolor=\"#0056EB\"\u003e \u003cmo  class=\"MathClass-bin\"\u003e−\u003c/mo\u003e \u003cmi  \u003ex\u003c/mi\u003e\u003c/mstyle\u003e\u003c/mtd\u003e                              \u003cmtd  class=\"align-even\"\u003e \u003cmo  class=\"MathClass-rel\"\u003e=\u003c/mo\u003e \u003cmn\u003e7\u003c/mn\u003e\u003cmstyle mathcolor=\"#E60000\"\u003e \u003cmo  class=\"MathClass-bin\"\u003e−\u003c/mo\u003e \u003cmn\u003e3\u003c/mn\u003e\u003c/mstyle\u003e\u003cmspace width=\"2em\"/\u003e\u003c/mtd\u003e                                     \u003cmtd  columnalign=\"right\" class=\"align-label\"\u003e\u003c/mtd\u003e                                     \u003cmtd  class=\"align-label\"\u003e                                      \u003cmspace width=\"2em\"/\u003e\u003c/mtd\u003e\u003c/mtr\u003e\u003cmtr\u003e\u003cmtd  columnalign=\"right\" class=\"align-odd\"\u003e\u003cmi  \u003ex\u003c/mi\u003e\u003c/mtd\u003e                                    \u003cmtd  class=\"align-even\"\u003e \u003cmo  class=\"MathClass-rel\"\u003e=\u003c/mo\u003e \u003cmn\u003e4\u003c/mn\u003e\u003cmspace width=\"2em\"/\u003e\u003c/mtd\u003e                                          \u003cmtd  columnalign=\"right\" class=\"align-label\"\u003e\u003c/mtd\u003e                                     \u003cmtd  class=\"align-label\"\u003e \u003cmspace width=\"2em\"/\u003e\u003c/mtd\u003e\u003c/mtr\u003e\u003c/mtable\u003e\u003c/math\u003e \u003c/b\u003e                                                                                               \u003c/div\u003e  \u003c/div\u003e      \u003cdiv class=\"tcolorbox fooqaexample\" id=\"tcolobox-1297\"\u003e     \u003cdiv class=\"tcolorbox-title\"\u003e                                                                                                                                                                                                                                          \u003cp class=\"indent\" \u003e     Example 8\u003c/p\u003e\u003c/div\u003e  \u003cdiv class=\"tcolorbox-content\"\u003e\u003cp class=\"noindent\" \u003e\u003cb\u003e\u003cspan  class=\"ec-lmbx-12x-x-144\"\u003eSolve the equation \u003c/span\u003e\u003cmath mathvariant=\"normal\"   xmlns=\"http://www.w3.org/1998/Math/MathML\"   display=\"inline\" \u003e\u003cmstyle mathvariant=\"bold-italic\"\u003e\u003cmstyle mathvariant=\"bold\"\u003e\u003cmn\u003e5\u003c/mn\u003e\u003cmi  \u003ex\u003c/mi\u003e \u003cmo  class=\"MathClass-bin\"\u003e−\u003c/mo\u003e \u003cmn\u003e1\u003c/mn\u003e\u003cmn\u003e1\u003c/mn\u003e \u003cmo  class=\"MathClass-rel\"\u003e=\u003c/mo\u003e \u003cmo  class=\"MathClass-bin\"\u003e−\u003c/mo\u003e\u003cmn\u003e3\u003c/mn\u003e \u003cmo  class=\"MathClass-bin\"\u003e+\u003c/mo\u003e \u003cmn\u003e4\u003c/mn\u003e\u003cmi  \u003ex\u003c/mi\u003e\u003c/mstyle\u003e\u003c/mstyle\u003e\u003c/math\u003e\u003cspan  class=\"ec-lmbx-12x-x-144\" type=\"punct\"\u003e.\u003c/span\u003e \u003c/p\u003e\u003cmath mathvariant=\"normal\"   xmlns=\"http://www.w3.org/1998/Math/MathML\"   display=\"block\" \u003e\u003cmtable  columnalign=\"left\" class=\"align-star\"\u003e                                   \u003cmtr\u003e\u003cmtd  columnalign=\"right\" class=\"align-odd\"\u003e\u003cmn\u003e5\u003c/mn\u003e\u003cmi  \u003ex\u003c/mi\u003e \u003cmo  class=\"MathClass-bin\"\u003e−\u003c/mo\u003e \u003cmn\u003e1\u003c/mn\u003e\u003cmn\u003e1\u003c/mn\u003e\u003c/mtd\u003e                                  \u003cmtd  class=\"align-even\"\u003e \u003cmo  class=\"MathClass-rel\"\u003e=\u003c/mo\u003e \u003cmo  class=\"MathClass-bin\"\u003e−\u003c/mo\u003e\u003cmn\u003e3\u003c/mn\u003e \u003cmo  class=\"MathClass-bin\"\u003e+\u003c/mo\u003e \u003cmn\u003e4\u003c/mn\u003e\u003cmi  \u003ex\u003c/mi\u003e\u003cmspace width=\"2em\"/\u003e\u003c/mtd\u003e                            \u003cmtd  columnalign=\"right\" class=\"align-label\"\u003e\u003c/mtd\u003e                            \u003cmtd  class=\"align-label\"\u003e                             \u003cmspace width=\"2em\"/\u003e\u003c/mtd\u003e\u003c/mtr\u003e\u003cmtr\u003e\u003cmtd  columnalign=\"right\" class=\"align-odd\"\u003e\u003cmn\u003e5\u003c/mn\u003e\u003cmi  \u003ex\u003c/mi\u003e\u003cmstyle mathcolor=\"#0056EB\"\u003e \u003cmo  class=\"MathClass-bin\"\u003e−\u003c/mo\u003e \u003cmn\u003e4\u003c/mn\u003e\u003cmi  \u003ex\u003c/mi\u003e\u003c/mstyle\u003e\u003c/mtd\u003e                            \u003cmtd  class=\"align-even\"\u003e \u003cmo  class=\"MathClass-rel\"\u003e=\u003c/mo\u003e \u003cmo  class=\"MathClass-bin\"\u003e−\u003c/mo\u003e\u003cmn\u003e3\u003c/mn\u003e\u003cmstyle mathcolor=\"#E60000\"\u003e \u003cmo  class=\"MathClass-bin\"\u003e+\u003c/mo\u003e \u003cmn\u003e1\u003c/mn\u003e\u003cmn\u003e1\u003c/mn\u003e\u003c/mstyle\u003e\u003cmspace width=\"2em\"/\u003e\u003c/mtd\u003e                                  \u003cmtd  columnalign=\"right\" class=\"align-label\"\u003e\u003c/mtd\u003e                                  \u003cmtd  class=\"align-label\"\u003e                                   \u003cmspace width=\"2em\"/\u003e\u003c/mtd\u003e\u003c/mtr\u003e\u003cmtr\u003e\u003cmtd  columnalign=\"right\" class=\"align-odd\"\u003e\u003cmi  \u003ex\u003c/mi\u003e\u003c/mtd\u003e                                   \u003cmtd  class=\"align-even\"\u003e \u003cmo  class=\"MathClass-rel\"\u003e=\u003c/mo\u003e \u003cmn\u003e8\u003c/mn\u003e\u003cmspace width=\"2em\"/\u003e\u003c/mtd\u003e                                           \u003cmtd  columnalign=\"right\" class=\"align-label\"\u003e\u003c/mtd\u003e                                  \u003cmtd  class=\"align-label\"\u003e \u003cmspace width=\"2em\"/\u003e\u003c/mtd\u003e\u003c/mtr\u003e\u003c/mtable\u003e\u003c/math\u003e \u003c/b\u003e                                                                                               \u003c/div\u003e  \u003c/div\u003e \u003cp class=\"indent\" \u003e     "},"siblings":[{"h1":"Why You Need Equations","path":"/encyclopedia/algebra/equations-and-inequalities/equations/linear-equations/why-you-need-equations"},{"h1":"What Is an Equation?","path":"/encyclopedia/algebra/equations-and-inequalities/equations/linear-equations/what-is-an-equation"},{"h1":"What Is a Variable?","path":"/encyclopedia/algebra/equations-and-inequalities/equations/linear-equations/what-is-a-variable"},{"h1":"How to Solve Equations (Change  Sides, change sign)","path":"/encyclopedia/algebra/equations-and-inequalities/equations/linear-equations/how-to-solve-equations-change-sides-change-sign"},{"h1":"How to Get Rid of the Number in Front of x","path":"/encyclopedia/algebra/equations-and-inequalities/equations/linear-equations/how-to-get-rid-of-the-number-in-front-of-x"},{"h1":"How to Solve Linear Equations (Combined Methods)","path":"/encyclopedia/algebra/equations-and-inequalities/equations/linear-equations/how-to-solve-linear-equations-combined-methods"},{"h1":"How to Get Rid of the Number Under x","path":"/encyclopedia/algebra/equations-and-inequalities/equations/linear-equations/how-to-get-rid-of-the-number-under-x"},{"h1":"How to Solve Equations with Parentheses","path":"/encyclopedia/algebra/equations-and-inequalities/equations/linear-equations/how-to-solve-equations-with-parentheses"},{"h1":"How to Solve Formulas for Specified Variables","path":"/encyclopedia/algebra/equations-and-inequalities/equations/linear-equations/how-to-solve-formulas-for-specified-variables"}],"type":"encyclopedia"},"topicOverview":[{"h1":"Numbers and 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Variable?","path":"/encyclopedia/algebra/equations-and-inequalities/equations/linear-equations/what-is-a-variable"},{"h1":"How to Solve Equations (Change  Sides, change sign)","path":"/encyclopedia/algebra/equations-and-inequalities/equations/linear-equations/how-to-solve-equations-change-sides-change-sign"},{"h1":"How to Get Rid of the Number in Front of x","path":"/encyclopedia/algebra/equations-and-inequalities/equations/linear-equations/how-to-get-rid-of-the-number-in-front-of-x"},{"h1":"How to Solve Linear Equations (Combined Methods)","path":"/encyclopedia/algebra/equations-and-inequalities/equations/linear-equations/how-to-solve-linear-equations-combined-methods"},{"h1":"How to Get Rid of the Number Under x","path":"/encyclopedia/algebra/equations-and-inequalities/equations/linear-equations/how-to-get-rid-of-the-number-under-x"},{"h1":"How to Solve Equations with 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