How do you solve #|-3x + 3| \leq 6#?

1 Answer
Mia
Feb 4, 2017

#x in [-1,3]#

Explanation:

Solving this inequality is based on the following property
#" "#
#absa<=brArr-b<=a<=b#
#" "#
#abs(-3x+3)<=6#
#" "#
#rArr-6<=-3x+3<=6#
#" "#
#-3x+3>=-6#
#" "#
And
#" "#
#-3x+3<=6#
#" "#
Solving the first inequality:
#" "#
#-3x+3>=-6#
#" "#
#rArr-3x>=-6-3#
#" "#
#rArr-3x>=-9#
#" "#
#rArrx<=(-9)/(-3)#
#" "#
#rArrx<=3#
#" "#
Solving the second inequality:
#" "#
#-3x+3<=6#
#" "#
#rArr-3x<=6-3#
#" "#
#rArr-3x<=3#
#" "#
#rArrx>=3/(-3)#
#" "#
#rArrx>=-1#

Hence, #x>=-1 and x<=3#
#" "#
Therefore, #x in [-1,3]#

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