Question

What is the solution set for `abs(2x – 3) – 10 = –1`?

Answer 1

`x = {-3,6}`

Explanation:

Start by isolating the modulus on one side of the equation

`|2x-3| - color(red)cancelcolor(black)(10) + color(red)cancelcolor(black)(10) = -1 + 10`

`|2x-3| = 9`

You are going to look at two cases for this equation

• `(2x-3)>0`, which means that you have

`|2x-3| = 2x-3`

and the equation is

`2x - 3 = 9`

`2x = 12 => x = 12/2 = color(green)(6)`

• `(2x-3)<0`, which will get you

`|2x-3| = -(2x-3) = -2x+3`

and the equation is

`-2x+3 = 9`

`-2x = 6 => x = 6/(-2) = color(green)(-3)`

Because you have no restriction for the values of `x` that you make for extraneous solutions, both values are valid solutions.