How do you solve $-5abs(x+13)+34<=9$ ?

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Answer 1 · 2015-06-14T21:09:24

Solve $-5|x + 13| + 34 <= 9$

$5|x + 13| >= 34 - 9$

$|x + 13| >= 5$

Separate solving into 2 cases.

a. $(x + 13) > 5 -> x > 5 - 13 -> x >= - 8$

b. $- (x + 13) = - x - 13 > 5 --> x <= -13 - 5 -> x <= - 18$
Graph

========|-18-----------------|-8=====|0=========

How do you solve -5abs(x+13)+34<=9-5abs(x+13)+34<=9?