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Chapter 2: Q. 428 (page 196)

Andrew is creating a rectangular dog run his back yard. The length of the dog is 18feet. The perimeter of the dog must be at least42feet and no more than72feet. Use the compound inequality to find the range of values for the width of the dog run.

Short Answer

Expert verified

The range of values for the width of the rectangle isw鈭�3,18.

Step by step solution

01

Step 1. Find the compound inequality. 

The rectangle has the length 18feet.

Perimeter is at least 42feet, and not more than72 feet.
Let wbe the width of the rectangle, and Pperimeter.

P=2路18+2路w

Perimeter is between 42and role="math" localid="1644903360687" 72, it follows:

42鈮�26+2W鈮�72

02

Step 2. Solve the compound inequality 

Break the compound inequality, it follows that:

42鈮�鈥�26+2wand鈥�26+2w鈮�鈥�72

First, solve 42鈮�鈥�26+2w:

Switch sides:

26+2w鈮�鈥�4226+2w-26鈮�鈥�42-262w鈮�鈥�162w2鈮�162w鈮�鈥�8

Now, solve 26+2w鈮�72:

Subtract 26from both sides:

26+2w-26鈮�鈥�72-262w鈮�鈥�462w2鈮�462w鈮�鈥�23

Merge overlapping intervals:

3鈮�w鈮�18

Interval notation:3,18

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