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

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Answer 1 · 2015-04-02T11:42:50

You solve for two possible scenarios:

(1)

$1/3 x-9>=0$ this is if $x>=27$
then the absolute will not have effect, and you solve normally for
$1/3 x-9=10->x-27=30->x=57$

(2)

$1/3 x-9<0$ this is if $x<27$
Then the absolute will turn this around into:
$9-1/3 x=10->27-x=30->x=-3$

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

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