How do you solve the inequality: $abs(x + 2) < 18$ ?

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Answer 1 · 2015-08-27T23:39:56

$x<16$
$x> -20$

$abs(x+2)<18$

Separate the inequality into two inequalities, one positive and one negative.

$x+2<18 and -(x+2)<18$

Positive Inequality

$x+2<18$

Subtract $2$ from both sides.

$x<18-2$ $=$

$x<16$

Negative Inequality

$-(x+2)<18$

$-x-2<18$

Add $2$ to both sides.

$-x<18+2$ $=$

$-x<20$

Multiply both sides times $-1$ .

$x> -20$

Solutions for $x$ .

$x<16$
$x> -20$

How do you solve the inequality: abs(x + 2) < 18 abs(x + 2) < 18?