Chapter 1.1, Problem 38E

(a)

To determine

To write: the statement “ $y$ is negative” in terms of inequality.

Answer to Problem 38E

  $y<0$

Explanation of Solution

Given information:

  $y$ is negative

Calculation:

Consider the given statement.

  $y$ is negative

Now, negative number is always less than 0.

So, $y<0$ .

(b)

To determine

To write: the statement “ $z$ is greater than 1” in terms of inequality.

Answer to Problem 38E

  $z>1$

Explanation of Solution

Given information:

  $z$ is greater than 1.

Calculation:

Consider the given statement.

  $z$ is greater than 1

Now, greater than sign is $\text{'}>\text{'}$ .

So, $z$ is greater than 1, in terms of an inequality can be written as

  $z>1$ .

(c)

To determine

To write: the statement “ $b$ is at most $8$ ” in terms of inequality.

Answer to Problem 38E

  $b\le 8$

Explanation of Solution

Given information:

  $b$ is at most $8$ .

Calculation:

Consider the given statement.

  $b$ is at most $8$

Now, for the word “at most” the required symbol is $\text{'}\le \text{'}$ .

So, $b$ is at most $8$ , in terms of an inequality can be written as

  $b\le 8$ .

(d)

To determine

To write: the statement “ $w$ is positive and less than equal to $17$ ” in terms of inequality.

Answer to Problem 38E

  $0<w\le 17$

Explanation of Solution

Given information:

  $w$ is positive and less than equal to $17$

Calculation:

Consider the given statement.

  $w$ is positive and less than equal to $17$

Now, greater than sign is $\text{'}>\text{'}$ and less than equal to symbol is $\text{'}\le \text{'}$ .

So, $w$ is positive and less than equal to $17$ , in terms of an inequality can be written as

  $0<w\le 17$ .

(e)

To determine

To write: the statement “the distance between $y$ and $\pi$ is at least $2$ ” in terms of inequality.

Answer to Problem 38E

  $\left|y-\pi \right|\ge 2$

Explanation of Solution

Given information:

The distance between $y$ and $\pi$ is at least $2$ .

Calculation:

Consider the given statement.

The distance between $y$ and $\pi$ is at least $2$ .

Distance between two points a and b can be written as

  $d\left(a,b\right)=\left|a-b\right|$

Now, for the word “at least” the required symbol is $\text{'}\ge \text{'}$ .

So, the distance between $y$ and $\pi$ is at least $2$ , in terms of an inequality can be written as

  $\begin{array}{l}d\left(y,\pi \right)\ge 2\\ \left|y-\pi \right|\ge 2\end{array}$ .