Question

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

Answer 1

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]}