Chapter 2.5, Problem 10E

To determine

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

Answer to Problem 10E

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

Explanation of Solution

Given information:

Given sentence

A number $r$ is no less than -1.5 and fewer than 9.5.

Calculation:

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

Recall that “no less than” means “greater than or equal to” is represented by the symbol “ $\ge$ ” and “fewer than” means “less than” and is represented by the symbol” $<$ ”.

So, $\text{'}r$ is no less than -1.5’ will be represented by $r\ge -1.5$ .

Also ‘ $r$ is fewer than 9.5’ will be represented by $r<9.5$ .

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

$r\ge -1.5$ and $r<9.5$

Thus, the required inequality is $r\ge -1.5$ and $r<9.5$

The graph of the inequality $-1.5\le r<9.5$ is shown below: