Question

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

$\left|x+1\right|\ge 1$

Short answer

The answer is$-2\ge x\ge 0.$

The interval notation of the answer is $(-\infty ,-2]\cup [0,\infty )$.

The graph of the solution set$-2\ge x\ge 0.$

Step-by-step solution

Step 1. Solve the absolute value inequalities.

$\begin{array}{c}\left|x+1\right|\ge 1\\ -1\ge x+1\ge 1\\ -2\ge x\ge 0\end{array}$

Hence, the solution set is$-2\ge x\ge 0.$

Step 2. Express the solution set in interval notation.

The interval notation of the solution set$-2\ge x\ge 0$ is$(-\infty ,-2]\cup [0,\infty )$

Step 3. Graph of solution set.

The graph of the solution set$-2\ge x\ge 0.$