How do you solve #3abs(2x-7)< 15#?

1 Answer
Apr 7, 2015

Answer:

The solution is #1 < x < 6#

Explanation:

To solve this inequality, we have to consider the expression inside the absolute value sign twice. Once treating it as positive and next treating it as negative.

  • Case 1

#3(2x-7) < 15#

#6x-21 < 15#

#6x < 36 implies x < 6#

  • Case 2

#3(-2x+7) < 15#

#-6x+21 < 15#

#6x-21 > -15#

#6x>6 implies x >1#

The solution is thus #1 < x < 6#