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

1 Answer
Aug 5, 2015

Answer:

#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.