Question

Andrew is creating a rectangular dog run in his back yard. The length of the dog run is 24 feet. The perimeter of the dog run must be at least 58 feet and no more than 96 feet. Use a compound inequality to find the range of values for the width of the dog run. Use

x when writing your inequality.

Answer 1

The perimeter of a rectangle is found by adding the length and width together twice, or 2l + 2w.

To find the range of values for the width of the dog run, we can set up a compound inequality using this formula:

2(24) + 2x ≥ 58 and 2(24) + 2x ≤ 96

Simplifying this, we get:

48 + 2x ≥ 58 and 48 + 2x ≤ 96

Subtracting 48 from each side:

2x ≥ 10 and 2x ≤ 48

Finally, dividing each side by 2:

x ≥ 5 and x ≤ 24

So the range of values for the width of the dog run is x ≥ 5 and x ≤ 24.