 Suggested languages for you:

Europe

Answers without the blur. Sign up and see all textbooks for free! Q33.

Expert-verified Found in: Page 252 ### Precalculus Mathematics for Calculus

Book edition 7th Edition
Author(s) James Stewart, Lothar Redlin, Saleem Watson
Pages 948 pages
ISBN 9781337067508 # Inequalities Place the correct symbol $\mathbf{\left(}\mathbf{<}\mathbf{,}\mathbf{>}\mathbf{,}\mathbf{\text{\hspace{0.17em}or\hspace{0.17em}}}\mathbf{=}\mathbf{\right)}$ in the space. a. $\mathbf{3}\mathbf{\text{\hspace{0.17em}}}\mathbf{_}\mathbf{_}\mathbf{_}\mathbf{\text{\hspace{0.17em}}}\frac{\mathbf{7}}{\mathbf{2}}$b. $\mathbf{-}\mathbf{3}\mathbf{\text{\hspace{0.17em}}}\mathbf{_}\mathbf{_}\mathbf{_}\mathbf{\text{\hspace{0.17em}}}\mathbf{-}\frac{\mathbf{7}}{\mathbf{2}}$c. $\mathbf{3.5}\mathbf{\text{\hspace{0.17em}}}\mathbf{_}\mathbf{_}\mathbf{_}\mathbf{\text{\hspace{0.17em}}}\frac{\mathbf{7}}{\mathbf{2}}$

a) The required symbol is$<$and the complete statement is $\mathbf{3}\mathbf{<}\frac{\mathbf{7}}{\mathbf{2}}$.

b) The required symbol is$>$and the complete statement is $\mathbf{-}\mathbf{3}\mathbf{>}\mathbf{-}\frac{\mathbf{7}}{\mathbf{2}}$.

c) The required symbol is$=$and the complete statement is $\mathbf{3.5}\mathbf{=}\frac{\mathbf{7}}{\mathbf{2}}$.

See the step by step solution

## Part a Step 1. Given information.

The given statement is:

$3___\frac{7}{2}$

## Part a Step 2. Write the concept.

If $\mathbit{a}$ is less than $\mathbit{b}$, then $\mathbit{a}\mathbf{<}\mathbit{b}$.

If $\mathbit{a}$ is greater than $\mathbit{b}$, then $\mathbit{a}\mathbf{>}\mathbit{b}$.

If $\mathbit{a}$ is equal to $\mathbit{b}$, then $\mathbit{a}\mathbf{=}\mathbit{b}$.

## part a Step 3. Determine the symbol.

The number $\frac{7}{2}$ can be written as $3.5$.

Clearly, 3 is less than $3.5$. So, role="math" localid="1648538469724" $3<3.5$ and $3<\frac{7}{2}$.

Thus, the required symbol is $<$ and the complete statement is $\mathbf{3}\mathbf{<}\frac{\mathbf{7}}{\mathbf{2}}$.

## Part b Step 1. Given information.

The given statement is:

$-3___-\frac{7}{2}$

## Part b Step 2. Write the concept.

If $\mathbit{a}$ is less than $\mathbit{b}$, then $\mathbit{a}\mathbf{<}\mathbit{b}$.

If $\mathbit{a}$ is greater than $\mathbit{b}$, then $\mathbit{a}\mathbf{>}\mathbit{b}$.

If $\mathbit{a}$ is equal to $\mathbit{b}$, then $\mathbit{a}\mathbf{=}\mathbit{b}$.

## Part b Step 3. Determine the symbol.

The number $-\frac{7}{2}$ can be written as $-3.5$.

Clearly, is the larger negative number between $-3$ and $-3.5$. It means $-3$ is greater than $-3.5$. So, $-3>-3.5$ and $-3>-\frac{7}{2}$.

Thus, the required symbol is $>$ and the complete statement is $\mathbf{-}\mathbf{3}\mathbf{>}\mathbf{-}\frac{\mathbf{7}}{\mathbf{2}}$.

## Part c Step 1. Given information.

The given statement is:

$3.5___\frac{7}{2}$

## Part c Step 2. Write the concept.

If $\mathbit{a}$ is less than $\mathbit{b}$, then $\mathbit{a}\mathbf{<}\mathbit{b}$.

If $\mathbit{a}$ is greater than $\mathbit{b}$, then $\mathbit{a}\mathbf{>}\mathbit{b}$.

If $\mathbit{a}$ is equal to $\mathbit{b}$, then $\mathbit{a}\mathbf{=}\mathbit{b}$.

## Part c Step 3. Determine the symbol.

The number $\frac{7}{2}$ can be written as $3.5$.

Clearly, $3.5$ is equal to $\frac{7}{2}$. So, $3.5=\frac{7}{2}$.

Thus, the required symbol is $=$and the complete statement is $\mathbf{3}\mathbf{.5}\mathbf{=}\frac{\mathbf{7}}{\mathbf{2}}$. ### Want to see more solutions like these? 