Chapter 1.6, Problem 53PPSE

Solution

The absolute value inequality that represents the circumference of the ball.

  $\left|x-28.75\right|<0.25$

Given:

The circumference of a basketball for college women must be from 28.5 in. to 29.0 in.

Concept Used:

• If there is the strict inequality symbol $<\text{ or}>$, then use a parenthesis $\left(\right)$ on the interval
• If there is the inequality symbol $\le \text{ or}\ge$, then use a bracket $\left[\right]$ on the interval
• To graph the endpoint with strict inequality $<\text{ or}>$, use the open parenthesis or a hollow circle at that endpoint.
• To graph the endpoint with inequality symbol $\le \text{ or}\ge$, use the bracket or a solid circle at that endpoint.
• Multiplying or dividing an inequality by a negative number reverse the inequality sign.
• The absolute value property: $\text{if }\left|x\right|>a,\text{then}x>a\text{ or }x<-a$
• The absolute value property: $\text{if }\left|x\right|<a,\text{then}-a<x<a$

Calculation:

Let x represents the circumference of the ball.

Note that the midpoint of 28.5 and 29 is 28.75 and the difference from this midpoint to each point is 0.25 in.

So, the absolute value inequality that represents the circumference of the ball is given by $\left|x-28.75\right|<0.25$ .

Thus, the required inequality is $\left|x-28.75\right|<0.25$ .