Chapter 8.7, Problem 55IP

(a)

To determine

Graph each inequality $b\ge 4\text{and}b\le 13$ on the same number line.

Answer to Problem 55IP

Explanation of Solution

Given:

Consider the inequalities $b\ge 4\text{and}b\le 13$ .

Graph each inequality $b\ge 4\text{and}b\le 13$ on the same number line.

Concept Used:

Graph each inequality $b\ge 4\text{and}b\le 13$ on the same number line.

  

(b)

To determine

Explain the meaning of the overlap region.

Answer to Problem 55IP

The overlapping section will be a solution to both inequalities.

Explanation of Solution

Given:

Consider the inequalities $b\ge 4\text{and}b\le 13$ .

Do the solution sets of the two inequalities overlap? If so, what does this overlapping area represent?

Concept Used:

The region included in both A and B, where the two sets overlap, is called the intersection of A and B, denoted by A n B.

The overlapping section will be a solution to both inequalities.

Thus,the overlapping section will be a solution to both inequalities.

(c)

To determine

Write a compound inequality for the situation.

Answer to Problem 55IP

  $4\le b\le 13$

Explanation of Solution

Given:

Consider the inequalities $b\ge 4\text{and}b\le 13$ .

A compound inequality is an inequality that combines two inequalities. Write a compound inequality for the situation.

Concept Used:

Compound inequality: $4\le b\le 13$