Emily is creating a rectangular garden in her backyard. The length of the garden is 12 feet. The perimeter of the garden must be at least 30 feet and no more than 64 feet. Use a compound inequality to find the range of values for the width w of the garden

w ≥ 3 AND w ≤ 20

Step-by-step explanation:

1. Let's review the information given to us to answer the question correctly:

Length of Emily's garden = 12 feet

Perimeter of Emily's garden should be at least 30 feet and no more than 64 feet

2. Use a compound inequality to find the range of values for the width w of the garden

Let's recall the perimeter formula of a rectangle:

Perimeter = 2 * Length + 2 * Width

Replacing the values we know:

30 = 2 * 12 + 2 Width

30 = 24 + 2 Width

30 - 24 = 2 Width

6 = 2 Width

6/2 = Width

Width = 3 feet

For having a 30 feet perimeter, we should have a 3 feet width. Now, let's calculate the width for a 64 feet perimeter, using the same formula:

64 = 2 * 12 + 2 Width

64 = 24 + 2 Width

64 - 24 = 2 Width

40 = 2 Width

40/2 = Width

Width = 20 feet

For having a 64 feet perimeter, we should have a 20 feet width. Now, let's write our compound inequality:

w ≥ 3 AND w ≤ 20