Question

How do you solve `abs(1/3x - 3) = 9`?

Answer 1

`x=-18" or "x=36`

Explanation:

`"the expression inside the absolute value bars can be"`
`"positive or negative leading to 2 possible solutions"`

`1/3x-3=9larrcolor(magenta)"positive value"`

`"add 3 to both sides"`

`rArr1/3x=9+3=12`

`"multiply both sides by 3"`

`rArrx=3xx12=36`

`-(1/3x-3)=9larrcolor(magenta)"negative value"`

`rArr-1/3x+3=9`

`"subtract 3 from both sides"`

`rArr-1/3x=9-3=6`

`"multiply both sides by "-3`

`rArrx=6xx-3=-18`

`color(blue)"As a check"`

Substitute these values into the left side of the equation and if equal to the right side then they are the solutions.

`x=36to|12-3|=|9|=9`

`x=-18to|-6-3|=|-9|=9`

`rArrx=-18" or "x=36" are the solutions"`