## Precalculus (6th Edition) Blitzer

$(-5,5)$
The solutions of $|u| \lt c$ are the numbers that satisfy $-c \lt u \lt c.$ 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 changes). --- $|x| \lt 5$ is equivalent to: $-5 \lt x \lt 5$ Both borders are excluded. The solution set is $(-5,5)$ .