(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement:

Suppose that a, b, x, and y are real numbers satisfying

a < x < b and a < y < b.

Show that |x - y| < b - a.

3. The attempt at a solution

We may start with the fact that:

i.) a < x < b

ii.) a < y < b

Subtracting a from all sides, we have that

i.) 0 = a - a < x - a < b - a

ii.) 0 = a - a < y - a < b - a

and

0 < x - a < b - a

0 < y - a < b - a

but I'm stuck here in justifying my steps. I thought about subtracting the inequalities from each other but that would just yield

0 < x - y < 0

which doesn't help my case :(

Any help and/or tips would be lovely!

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# Homework Help: Proving a Statement

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