Need help with college algebra. I must show my work on the problems.?

Question

Find and example for which Ia-bI>IaI-IbI, and and example for which Ia-bI=IaI-IbI. Then prove that Ia-bI>or equal to IaI-IbI for all a,b.

Answer 1

If a is positive and b is negative, or vice versa, then /a-b/>/a/-/b/. If a and b are both positive or both negative, then /a-b/=/a/-/b/. This covers all possible cases of a and b, thus /a-b/>=/a/-/b/.

Answer 2

|a - b| = |a| - |b| if a and b are both positive or both negative. If either a is negative or b is negative, then |a - b| is always ≥ |a| - |b|, because the numbers inside the absolute value sign on the left will always add together.