How do you solve #|5x + 3| <= 13#?

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Answer 1 · 2015-12-01T17:39:55

#x<=2# and #x>=-16/5#

Since we are dealing with absolute value we will have to solve the following two inequalities

#5x+3<=13# and #-(5x+3)<=13#

Solving the first one

Substract #3# from both sides

#5x+3-3<=13-3#

#5x<=10#

Dividing by both sides by #5#

#x<=2#

Now solving the second one

Distribute the negative sign on the left hand side

#-5x-3<=13#

Add #3# to both sides

#-5x-3+3<=13+3#

#-5x<=16#

Divide both sides by #-5#
Since we are dividing through by a negative number we must flip the inequality sign.

#x>=-16/5#