#### Answer

$[-1,3]$

#### Work Step by Step

The solutions of $|u| \lt c $ are the numbers that satisfy $-c \lt u \lt c.$
For compound inequalities, the idea is to isolate $x$ in the middle. Adding, subtracting or multiplying/dividing with a positive number preserves order (the inequality symbols remain).
Multiplying/dividing with a negative number inverts the order (the inequality symbols change).
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$|x-1|\leq 2$
This is equivalent to
$-2\leq x-1\leq 2\qquad $ ... add $1$ to all parts
$-1\leq x\leq 3$
Both borders are included:
The solution set is $[-1,3]$