Chapter 2.5, Problem 9E

To determine

To write: the sentence as an inequality and to sketch the graph of the inequality,

Answer to Problem 9E

The required inequality is $m>-7\frac{2}{3}$ and $m\le -10$ .

Explanation of Solution

Given information:

Given sentence

A number $m$ is more than $-7\frac{2}{3}$ or at most -10.

Calculation:

Note that a compound inequality is an inequality formed by combining two inequalities with the word “and” or the word “or”.

Recall that “more than” is represented by the symbol “ $>$ ” and “at most” is represented by the symbol” $\le$ ”.

So, $\text{'}m$ is more than $-7\frac{2}{3}$ ’ will be represented by $m>-7\frac{2}{3}$ .

Also ‘ $m$ is at most -10’ will be represented by $m\le -10$ .

Combine the above two inequalities using the word “or” to get,

$m>-7\frac{2}{3}$ and $m\le -10$

Thus, the required inequality is $m>-7\frac{2}{3}$ and $m\le -10$ .

The graph of the inequality $m>-7\frac{2}{3}$ and $m\le -10$ is shown below: