Question

How do you solve `abs(2x - 6) = 12`?

Answer 1

`x=-3, 9`

Explanation:

`2x-6=12 and 2x-6=-12`

`2x=18 and 2x=-6`

`x=9 and x=-3`

Answer 2

`x=-3" or "x=9`

Explanation:

`"the expression inside the absolute value can be positive"`
`"or negative, thus there are 2 possible solutions"`

`color(magenta)"Positive value"`

`2x-6=12`

`"add 6 to both sides"`

`rArr2x=18rArrx=9`

`color(magenta)"Negative value"`

`-(2x-6)=12`

`rArr-2x+6=12`

`"subtract 6 from both sides"`

`rArr-2x=6`

`"divide both sides by "-2`

`rArrx=-3`

`color(blue)"As a check"`

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

`|(2xx9)-6|=|18-6|=|12|=12`

`|(2xx-3)-6|=|-6-6|=|-12|=12`

`rArrx=-3" or "x=9" are the solutions"`