Absolute Value Inequalities

Recall the definition of absolute value. If $c$ is any positive real number, there are four absolute value inequality rules for you to know. If you interpret $|x|$ as the distance from $x$ to $0$, these inequalities should be easy to remember.
  1. If $|x| < c$, then $-c < x < c$.
    $|x| < 2$ means $-2 < x < 2$.
  2. If $|x| > c$, then $x < -c$ or $x > c$.
    $|x| > 2$ means $x < -2$ or $x > 2$.
  3. If $|x| \leq c$, then $-c \leq x \leq c$
    $|x| \leq 2$ means $-2 \leq x \leq 2$.
  4. If $|x| \geq c$, then $x \leq -c$ or $x \geq c$
    $|x| \geq 2$ means $x \leq -2$ or $x \geq 2$.
Absolute value inequalities.

Problem Set 2.8

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