Chapter 1 - Expressions, Equations, and Inequalities - 1-6 Absolute Value Equations and Inequalities - Practice and Problem-Solving Exercises - Page 48: 89

Absolute value inequalities of the form $|x| \lt a$ are equivalent to “AND” compound inequalities. Absolute value inequalities of the form $|x| \gt a$ are equivalent to “OR” compound inequalities. These also apply with the symbols $\leq$ and $\geq$.

$|x| \lt a$ is equivalent to $x \lt a$ AND $x \gt -a$. $|x| \gt a$ is equivalent to $x \gt a$ OR $x \lt -a$. These also apply with the symbols $\leq$ and $\geq$.