How do you solve $abs(2x+9) ≤ 3$ ?

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Answer 1 · 2017-02-28T23:11:54

$-6 le x le-3$

Because it has the absolute value sign, you can assume there are two equations:
$2x+9le3$
and
$-(2x+9)le3$

Lets solve for the first one.
$2xle-6$
$xle-3$

Now onto the second one.
$2x+9ge-3$
$2xge-12$
$xge-6$

Now combine the two answers.
$xle-3$ and $xge-6$ for $-6lexle-3$

How do you solve abs(2x+9) ≤ 3abs(2x+9) ≤ 3?