Question

Solve the absolute value inequality. Express the answer using interval notation and graph the solution set.

$\left|\frac{x-2}{3}\right|<2$

Short answer

The answer is $-4<x<8$.

The interval notation of the answer is $\left(-4,8\right)$.

The graph of the solution set$-4<x<8$

Step-by-step solution

Step 1. Solve the absolute value inequalities.

$\begin{array}{c}\left|\frac{x-2}{3}\right|<2\\ -2<\frac{x-2}{3}<2\\ -6<x-2<6\\ -4<x<8\end{array}$

Hence, the solution set is $-4<x<8$.

Step 2. Express the solution set in interval notation.

The interval notation of the solution set $-4<x<8$is $\left(-4,8\right)$.

Step 3. Graph of solution set.

The graph of the solution set$-4<x<8$