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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.

Respuesta :

alphabetsam
Let's start with the given:
[tex]a<b[/tex] for any a, b such that a and b are real numbers.

Multiplying by [tex]\frac{1}{a}[/tex] on both sides:
[tex](\frac{1}{a})a=1<(\frac{1}{a})b[/tex]

Now multiply by [tex]\frac{1}{b}[/tex] on both sides:
[tex](\frac{1}{b})1=\frac{1}{b}<(\frac{1}{a})b(\frac{1}{b})=\frac{1}{a}[/tex]

Then we have:
[tex]\frac{1}{b}<\frac{1}{a}[/tex]

Then the answer must be c.

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