# Absolute value inequality

1. Nov 7, 2014

### OceanSpring

• Member warned about not using the homework template
Question:
True or False If x^2<4 then |x|<=2

My solution:
I get -2<x<2 when I solve the problem so it should be false. Yet the text says its true? Is this a mistake? If |x| is equal to 2 then it should be a closed interval, not an open interval which seems to be correct to me.

Last edited by a moderator: Nov 7, 2014
2. Nov 7, 2014

### Staff: Mentor

x2 < 4 is equivalent to -2 < x < 2 or |x| < 2. What the text has appears to be a typo.

3. Nov 7, 2014

### PeroK

It's probably a typo, although logically it is true:

If $x^2 < 4$ then $|x| < 2$ hence $|x| \le 2$

If it were false, then there would be $x$ with $|x| > 2$ yet $x^2 < 4$