How do you solve the inequality: #abs(x - 8) < 5#?

1 Answer
Stefan V.
Aug 14, 2015

#3 < x < 13#

Explanation:

In order to solve this absolute value inequality, you need totake into account the two possible signs the expression inside the modulus can have

  • #x-8>0 implies |x-8| = x - 8#

The inequality will become

#x - 8 < 5#

#x < 13#

  • #x - 8 < 0 implies |x - 8| = -(x-8)#

This time, the inequality will be

#-(x-8) < 5#

#-x + 8 < 5#

#x > 3#

So, the solution set for this inequality will include any value of #x# that is bigger than #3# and smaller than #13#.

This means that you have #3 < x < 13#, or #x in (3, 13)#.

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