Question

5. Suppose that a and b are both real numbers such that a < b. What can you conclude about the inequality 1/a < 1/b?

a. 1/a < 1/b is always true.
b. 1/a < 1/b is sometimes true.
c. 1/a < 1/b is never true.
d. A valid conclusion cannot be determined from the given information.

Answer 1

Let's start with the given:

`a<b` for any a, b such that a and b are real numbers.

Multiplying by
`(1)/(a)` on both sides:

`((1)/(a))a=1<((1)/(a))b`

Now multiply by
`(1)/(b)` on both sides:

`((1)/(b))1=(1)/(b)<((1)/(a))b((1)/(b))=(1)/(a)`

Then we have:

`(1)/(b)<(1)/(a)`

Then the answer must be c.