Try the fastest way to create flashcards
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

Verified
Step 1
1 of 2

Let'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 $\color{#c34632}{\frac{1}{-1}<\frac{1}{-2}}$.

## Recommended textbook solutions

#### Thomas' Calculus

14th EditionISBN: 9780134438986 (11 more)Christopher E Heil, Joel R. Hass, Maurice D. Weir
10,142 solutions

#### Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach

10th EditionISBN: 9781285464640 (4 more)Tan, Soo
5,088 solutions

#### Calculus: Early Transcendentals

8th EditionISBN: 9781285741550James Stewart
11,083 solutions

#### Calculus: Early Transcendentals

9th EditionISBN: 9781337613927 (3 more)Daniel K. Clegg, James Stewart, Saleem Watson
11,050 solutions