Chapter 1, Problem 8CCSR

Solution

To write an absolute value inequality that represents the height of the handbag.

  $\left(\text{G}\right)\left|h-17\right|\le 1$

Given:

The height of the handbag must be between 16 in. and 18 in. The desired height is 17 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 h represents the height of the handbag.

Note that the height of the handbag must be between 16 in. and 18 in. and the desired height of bag is 17 in.

Since the variance in height is 1 in. from the desired height of the handbag, the absolute value inequality that represents the situation is given by $\left|h-17\right|\le 1$ .

Thus, the required absolute value inequality that represent the given situation is $\left|h-17\right|\le 1$ .