Question

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

$\frac{1}{2}\left|x\right|\ge 1$

Short answer

The answer is$-2\ge x\ge 2.$

The interval notation of the answer is $(-\infty ,2]U[2,\infty )$.

The graph of the solution set is $-2\ge x\ge 2.$

Step-by-step solution

Step 1. Solve the absolute value inequalities.

$\begin{array}{c}\frac{1}{2}\left|x\right|\ge 1\\ \left|x\right|\ge 2\\ -2\ge x\ge 2\end{array}$

Hence, the solution set is$-2\ge x\ge 2.$

Step 2. Express the solution set in interval notation.

The interval notation of the solution set$-2\ge x\ge 2$ is $(-\infty ,2]U[2,\infty )$.

Step 3. Graph of solution set.

The graph of the solution set is$-2\ge x\ge 2.$