How do you solve #|5x + \frac{1}{2} | - 4< 3#?

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Answer 1 · 2016-09-20T20:04:23

#- (3) / (2) < x < (13) / (10)#

We have: #abs(5 x + (1) / (2)) - 4 < 3#

First, let's add #4# to both sides of the inequality:

#=> abs(5 x + (1) / (2)) < 7#

Then, we will split the inequality into two parts:

#=> 5 x + (1) / (2) < 7#

#=> 5 x < (13) / (2)#

#=> x < (13) / (10)#

or

#=> 5 x + (1) / (2) > - 7#

#=> 5 x > - (15) / (2)#

#=> x > - (3) / (2)#

Therefore, the solution set to this inequality is #- (3) / (2) < x < (13) / (10)#.