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

Question

1997 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-08-27T23:39:56

$x < 16$ $x<16$
$x > - 20$ $x> -20$

$| x + 2 | < 18$ $abs(x+2)<18$

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

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

Positive Inequality

$x + 2 < 18$ $x+2<18$

Subtract $2$ $2$ from both sides.

$x < 18 - 2$ $x<18-2$ $=$ $=$

$x < 16$ $x<16$

Negative Inequality

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

$- x - 2 < 18$ $-x-2<18$

Add $2$ $2$ to both sides.

$- x < 18 + 2$ $-x<18+2$ $=$ $=$

$- x < 20$ $-x<20$

Multiply both sides times $- 1$ $-1$ .

$x > - 20$ $x> -20$

Solutions for $x$ $x$ .

$x < 16$ $x<16$
$x > - 20$ $x> -20$

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