Precalculus Review

Absolute Value Inequalities

Recall the definition of absolute value. If

c

$c$ is any positive real number, there are four absolute value inequality rules for you to know. If you interpret

| x |

$|x|$ as the distance from

x

$x$ to

0

$0$ , these inequalities should be easy to remember.

If $|x| < c$ , then $-c < x < c$ .

$|x| < 2$ means $-2 < x < 2$ .
If $|x| > c$ , then $x < -c$ or $x > c$ .

$|x| > 2$ means $x < -2$ or $x > 2$ .
If $|x| \leq c$ , then $-c \leq x \leq c$

$|x| \leq 2$ means $-2 \leq x \leq 2$ .
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.

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