Answer:
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
