What is the solution to the inequality #abs(2x-1) <9#?

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Answer 1 · 2015-08-17T00:43:52

#x > -4# and #x < 5#

#-4 < x < 5#

When solving an inequality with absolute value we really have
two inequalities

#2x-1< 9# and #-(2x-1)< 9#

Solving each one as follows

#2x-1 < 9#

#2x<10#

#x < 5#

Now for the next one

#-(2x-1)< 9#

#2x-1> -9# Dividing by the negative flips the inequality sign

#2x > -8#

#x > -4#