# Solve absolute value inequality. |x−1|≤2

Anne Wacker

## Answered question

2021-12-10

Solve absolute value inequality.

$|x-1|\le 2$

### Answer & Explanation

Step 1

$|x-1|\le 2$

We know

$x-1\le 2\text{}{\textstyle \phantom{\rule{1em}{0ex}}}\text{and}{\textstyle \phantom{\rule{1em}{0ex}}}\text{}x-1\ge -2$

Step 2

$x-1\le 2$ (Condition 1)

$x-1+1\le 2+1$ (Add 1 to both sides)

$x\le 3$

$x-1\ge -2$ (Condition 2)

$x-1+1\ge -2+1$ (Add 1 to both sides)

$x\ge -1$

Answer:

$x\le 3\text{}{\textstyle \phantom{\rule{1em}{0ex}}}\text{and}{\textstyle \phantom{\rule{1em}{0ex}}}\text{}x\ge -1$

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