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

1 Answer
Aug 5, 2015

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.