# Prove that if a>0, then the absolute value of x …

**Question**

Prove that if a>0, then the absolute value of x < a iff -a<x<a?

**Answer**

a > 0.

In order for | x | < a, we must have either

if x is negative then its ‘value’ must be ‘less negative’ than

‘-a’ and hence ‘smaller in absolute value’ meaning x < – a. giving the lower bound above, -a < x.

if x is positive, then its value must be less than the positive value ‘a’, implying, x <a.

Thus we have -a < x < a.