How do you solve the inequality: # 0 < 2y + 8 < 12#?

1 Answer
Aug 8, 2015

Answer:

#-4 < y < 2#

Explanation:

Things you can do to both sides of an inequality while maintaining the validity of the inequality:

  • Add or subtract any amount to/from both sides
  • Multiply or divide by any amount greater than zero

While it is possible to solve a compound expression (with more than one inequality symbol) it is probably safer to handle the two pieces separately and then recombine.

#0 < 2y + 8 < 12#
will be treated as
Part 1: #0 < 2y + 8 # and
Part 2: #2y + 8 < 12#

Part 1
#0 < 2y +8#
#rarr##color(white)("XXXX")##-8 < 2y#
#rarr##color(white)("XXXX")##-4 < y#

Part 2
#2y + 8 < 12#
#rarr##color(white)("XXXX")##2y < 4#
#rarr##color(white)("XXXX")##y < 2#

Recombining
#color(white)("XXXX")##-4 < y < 2#