What is the solution set for #abs(3x – 2) < 7#?

1 Answer
Aug 22, 2015

Answer:

#x in (-5/3, 3)#

Explanation:

Since you're dealing with the absolute value of a variable expression, you must take into account the fact that this expression can be negative or positive.

  • #3x-2>0 implies |3x-2| = 3x-2#

The inequality becomes

#3x-2 < 7#

#3x < 9 implies x < 3#

  • #(3x-2)<0 implies |3x-2| = -(3x-2)#

This time, you get that

#-(3x-2) < 7#

#-3x + 2 < 7#

#-3x < 5 implies x > -5/3#

This means that your original inequality will be true for any value of #x# that is smaller than #3# and bigger than #-5/3#.

The solution interval will thus be #(-5/3, 3)#.