Question

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

$\left|2x\right|>7$

Short answer

The answer is$-\frac{7}{2}<x<\frac{7}{3}.$

The interval notation of the answer is$\left(-\infty ,-\frac{7}{2}\right)U\left(\frac{7}{2},\infty \right)$

The graph of the solution set $-\frac{7}{2}<x<\frac{7}{2}.$

Step-by-step solution

Step 1. Solve the absolute value inequalities.

$\begin{array}{c}\left|2x\right|>7\\ -7>2x>7\\ -\frac{7}{2}>x>\frac{7}{2}\end{array}$

Hence, the solution set is$-\frac{7}{2}<x<\frac{7}{2}.$

Step 2. Express the solution set in interval notation.

The interval notation of the solution set $-\frac{7}{2}<x<\frac{7}{2}$is$\left(-\infty ,-\frac{7}{2}\right)U\left(\frac{7}{2},\infty \right)$

Step 3. Graph of solution set.

The graph of the solution set $-\frac{7}{2}<x<\frac{7}{2}.$