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