Checking the Answer

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 $\frac{x}{3} + 1 = 4 - \frac{2 x}{3}$

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}{l} 4 - \frac{2 x}{3} & = 4 - \frac{2 \cdot 3}{3} \\ = 4 - \frac{6}{3} \\ = 4 - 2 \\ = 2 \end{array}

4 - \frac{2 x}{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.

Activities 6

Activities 7