What is the solution set for #abs(3x – 24) ≤ 27#?

1 Answer
Aug 12, 2015

Answer:

#-1 <= x <= 17#

Explanation:

Part 1
If #(3x-24) < 0#
then #abs(3x-24) <= 27#
#rArr##color(white)("XXXX")##24-3x <= 27#

Adding #3x# to both sides
#color(white)("XXXX")##color(white)("XXXX")##24 <= 27 +3x#

Subtracting #27# from both sides
#color(white)("XXXX")##color(white)("XXXX")##-3 <= 3x#

Dividing by #3#
#color(white)("XXXX")##color(white)("XXXX")##-1 <= x#

Part 2
If #(3x-24) >= 0#
then #abs(3x-24) <= 27#
#rArr##color(white)("XXXX")##3x-24 <= 27#

Adding #24# to both sides
#color(white)("XXXXXXXX")##3x <= 51#

Dividing by #3#
#color(white)("XXXXXXXX")##x <= 17#

Combining Part 1 and Part 2
#color(white)("XXXX")##-1 <= x <= 17#