Question

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

$\left|5x-2\right|<8$

Short answer

The answer is $-\frac{6}{5}<x<2$.

The interval notation of the answer is $\left(-\frac{6}{5},2\right)$.

The graph of the solution set $-\frac{6}{5}<x<2$.

Step-by-step solution

Step 1. Solve the absolute value inequalities.

$\begin{array}{c}\left|5x-2\right|<8\\ -8<5x-2<8\\ -6<5x<10\\ -\frac{6}{5}<x<2\end{array}$

Hence, the solution set is $-\frac{6}{5}<x<2$.

Step 2. Express the solution set in interval notation.

The interval notation of the solution set$-\frac{6}{5}<x<2$ is $\left(-\frac{6}{5},2\right)$.

Step 3. Graph of solution set.

The graph of the solution set $-\frac{6}{5}<x<2$.