Chapter 1 - 1.7 - Linear Inequalities in One Variable - 1.7 Exercises - Page 138: 83

$|x+3|\lt4$

$|u|\lt a~↔~-a\lt u\lt a$ $|u|\leq a~↔~-a\leq u\leq a$ $|u|\gt a~↔~u\lt-a~or~u\gt a$ $|u|\geq a~↔~u\leq-a~or~u\geq a$ The numbers must be greater than -7 and less than 1: $-7\lt x\lt1$ $-7+3\lt x+3\lt1+3$ $-4\lt x+3\lt4$ $|x+3|\lt4$