What is the solution set for #absx < 15#?

1 Answer
Stefan V.
Aug 14, 2015

#-15 < x < 15#

Explanation:

All you really have to do to solve this absolute value inequality is to take into account the two possible signs #x# can have.

  • #x>0 implies |x| = x#

In this case, the inequality becomes

#x < 15#

  • #x<0 implies |x| = -x#

This time, you have

#-x < 15 implies x > -15#

So, the solution set to this inequality will include any value of #x# that simultaneously satisfies these conditions, #x > -15# and #x<15#.

Therefore, the solution set will be #-15 < x < 15#, or #x in (-15, 15)#.

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