Algebra
Testing solutions to equations is a method you use to check if the solution you got is correct. After you solve the equation, you can check if the answer is correct by inserting the solution into both sides. You then check if the value of the expression on the left hand side (LHS) is equal to the value of the expression on the right hand side (RHS).
Rule
Testing a solution to an equation
- 1.
- Write the left side of the equation.
- 2.
- When you solved the equation you found a value for . Insert the value in for the in the expression from Item 1. Then calculate.
- 3.
- Write the right side of the equation.
- 4.
- When you solved the equation you found a value for . Insert the value in for the in the expression from Item 3. Then calculate.
- 5.
- If one of the sides doesn’t have , that’s okay. Just calculate that side like normal.
- 6.
- If you find that your calculations of the left side and the right side are equal, you have found the correct solution!
Think About This
It’s very important that you really know what the equal sign means.
The equal sign demands that what is on each side is equal to another. You can read it from left to right, but also from right to left.
Example 1
Test the solution to the equation
You solved and got . and .
You check if is a solution to the equation :
| LHS | RHS |
Since LHS RHS, you know that the solution is correct.
Example 2
Test the solution to the equation
We solved the equation and got . The and the . Check if is a solution to the equation .
| LHS | RHS |
Since LHS RHS, you know that the answer is correct. We know that when LHS RHS, the solution is correct!