Question

Nidhi is creating a rectangular garden in her back yard. The length of the garden is 10 feet. The perimeter of the garden must be at least 40 feet and no more than 76 feet. Write and solve a compound inequality to find the range of values for the width, w, of the garden.

Answer 1

To find the range of values for the width, w, of the garden, use a compound inequality. The range for the width is 10 ≤ w ≤ 28 feet.

Step-by-step explanation:

To find the range of values for the width, w, of the garden, we need to write and solve a compound inequality. The length of the garden is given as 10 feet and the perimeter of the garden must be at least 40 feet and no more than 76 feet. Let's set up the compound inequality:

40 ≤ 2(length + width) ≤ 76

Substituting the given length of 10, we get:

40 ≤ 2(10 + width) ≤76

Simplifying and solving the compound inequality gives us:

20 ≤ 10 + width ≤ 38

Subtracting 10 from all parts of the inequality, we get:

10 ≤ width ≤ 28

Therefore, the range of values for the width, w, of the garden is 10 ≤ w ≤ 28 feet.