## Precalculus (6th Edition) Blitzer

$[-1,3]$
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). --- $|x-1|\leq 2$ 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 $[-1,3]$