Given 2 < a < 3 and 5 < b < 6 Find:
a. __ < a-b < __
5 < b < 6
multiplying through by -1 flips inequalities:
-5 > -b > -6
That is equivalent to
-6 < -b < -5
We add that term by term to 2 < a < 3
2 < a < 3
-6 < -b < -5
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-4 < a-b < -2
b. __ < a/b < __
is an interval of all positive numbers,
The interval of reciprocals are in the opposite
order of inequality:
and that is equivalent to
So we multiply 2 < a < 3 term by term by that:
Edwin
