Checking the Answer

After you’ve solved an equation, you can check the answer by substituting $x$ in the equation with the answer, and 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 $\frac{x}{3} + 1 = 4 - \frac{2 x}{3}$

Substituing $x = 3$ 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 \times 3}{3} \\ = 4 - \frac{6}{3} \\ = 4 - 2 \\ = 2 . \end{array}

4 - \frac{2 x}{3} = 4 - \frac{2 \times 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.

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