  Math Topics

After you’ve solved an equation, you can check the answer by substituting the answer you got for $x$ into the equation. Then, you check to see if you get the same result on both the left-hand and the right-hand side.

Example 1

Check if $x=3$ is a solution to $\frac{x}{3}+1=4-\frac{2x}{3}$

Substituting $x=3$ on the left-hand side gives you

 $\frac{x}{3}+1=\frac{3}{3}+1=1+1=2$

Substituting $x=3$ on the right-hand side gives you

$\begin{array}{llll}\hfill 4-\frac{2x}{3}& =4-\frac{2\cdot 3}{3}\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\\ \hfill & =4-\frac{6}{3}\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\\ \hfill & =4-2\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\\ \hfill & =2\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\end{array}$

 $4-\frac{2x}{3}=4-\frac{2\cdot 3}{3}=4-\frac{6}{3}=4-2=2$

This means that both the left-hand side and right-hand side are equal to 2 when you substitute 3 for $x$. You’ve now checked the answer, and since both sides are equal, it means that $x=3$ is a correct solution.

Note! It is possible for there to be more than one solution for $x$ in many equations, especially those where $x$ is raised to a power.