How to Check Solutions to an Equation

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Encyclopedia>Algebra>Equations and Inequalities>Equations>Techniques>How to Check Solutions to an Equation

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 $x$ . Insert the value in for the $x$ 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 $x$ . Insert the value in for the $x$ in the expression from Item 3. Then calculate.
5.: If one of the sides doesn’t have $x$ , 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

x + 2 = 5

You solved $x + 2 = 5$ and got $x = 3$ . $The left side i s = x + 2$ and $The right side = 5$ .

You check if $x = 3$ is a solution to the equation $x + 2 = 5$ :


LHS	RHS

$x + 2$	$5$

$= 3 + 2$

$= 5$

Since LHS $=$ RHS, you know that the solution $x = 3$ is correct.

Example 2

Test the solution to the equation

2 x + 3 = 7 + x

We solved the equation $2 x + 3 = 7 + x$ and got $x = 4$ . The $LHS = 2 x + 3$ and the $RHS = 7 + x$ . Check if $x = 4$ is a solution to the equation $2 x + 3 = 7 + x$ .


LHS	RHS

$2 x + 3$	$7 + x$

$= 2 \cdot 4 + 3$	$= 7 + 4$

$= 8 + 3$	$= 11$

$= 11$

Since LHS $=$ RHS, you know that the answer $x = 4$ is correct. We know that when LHS $=$ RHS, the solution is correct!

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