What is the solution set for absx < 15|x|<15?

1 Answer
Stefan V.
Aug 14, 2015

-15 < x < 15−15<x<15

Explanation:

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

  • x>0 implies |x| = xx>0⇒|x|=x

In this case, the inequality becomes

x < 15x<15

  • x<0 implies |x| = -xx<0⇒|x|=−x

This time, you have

-x < 15 implies x > -15−x<15⇒x>−15

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

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

Related questions
See all questions in Absolute Value Equations
Impact of this question
2157 views around the world
You can reuse this answer
Creative Commons License