Evelyn is creating a rectangular garden in her backyard. The length of the garden is 11 feet. The perimeter of the garden must be at least 56 feet and no more than 82 feet. Use a compound inequality to find the range of values for the width w of the garden.

The range of values for the width w of the garden is 17 ≤ w ≤ 30.

Step-by-step explanation:

Given,

The length of the garden = 11 feet.

The perimeter of the garden = 56 feet (at least is the minimum value)

The perimeter of the garden = 82 feet (not more than is the maximum value)

step 1:

Perimeter of a rectangle = 2 (length + width)

⇒ 56 = 2 (11 + width)

⇒ 56 = 22 + 2 width

⇒ 34 = 2 width

⇒ width = 34/2

∴ width = 17 feet

step 2:

Perimeter of a rectangle = 2 (length + width)

⇒ 82 = 2 (11 + width)

⇒ 82 = 22 + 2 width

⇒ 60 = 2 width

⇒ width = 60/2

∴ width = 30 feet

step 3:

The range of values for width 'w' is 17 ≤ w ≤ 30.