How do you solve and graph #abs(2x+1)<5#?

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Answer 1 · 2018-06-16T11:49:29

The solutions are #x in (-3,2)#

Solving an inequality with absolute values

#|2x+1|<5#

Therefore,

#{(2x+1<5),(-2x-1<5):}#

#<=>#, #{(2x+1-5<0),(-2x-1-5<0):}#

#<=>#, #{(2x-4<0),(-2x-6<0):}#

#<=>#, #{(x<2),(x>-3):}#

The solutions are

#x in (-3,2)#

graph{|2x+1|-5 [-8.89, 8.89, -4.444, 4.445]}