# How do you solve abs[1/3x-9]=10?

Apr 2, 2015

You solve for two possible scenarios:

(1)

$\frac{1}{3} x - 9 \ge 0$ this is if $x \ge 27$
then the absolute will not have effect, and you solve normally for
$\frac{1}{3} x - 9 = 10 \to x - 27 = 30 \to x = 57$

(2)

$\frac{1}{3} x - 9 < 0$ this is if $x < 27$
Then the absolute will turn this around into:
$9 - \frac{1}{3} x = 10 \to 27 - x = 30 \to x = - 3$

graph{|x/3 -9| [-8.8, 73.37, -4, 37.12]}