## Related questions with answers

Question

Suppose a and b are real numbers other than zero and that a>b. State whether the inequality is true or false for all real numbers a and b. $\frac{1}{a}>\frac{1}{b}$

Solution

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1 of 2Let's solve given problem

$\frac{1}{a}>\frac{1}{b}$

First, we will substract $\frac{1}{b}$ from both sides of inequality

$\frac{1}{a}-\frac{1}{b}>0$

LCD is $ab$

$\frac{b-a}{ab}>0$

If $b-a<0$ $(a>b)$ and $ab>0$ then

$\frac{b-a}{ab}<0$

so the given statement is $\color{#c34632}{\text{not true}}$ for all real numbers $a$ and $b$ other than zero and that $a>b$. For example, if $a=-1$ $b=-2$ then $\color{#c34632}{\frac{1}{-1}<\frac{1}{-2}}$.

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