Question

Use a compound inequality to find the range of values for the width of Dave's workshop, given that the length is fixed at 9 feet and the area should be between 90 and 126 square feet.

A. 6 ≤ width ≤ 14
B. 3 < width < 15
C. 9 ≤ width ≤ 14
D. 3 ≤ width < 15

Answer 1

After setting up the compound inequality with the area limits and the fixed length, we find that the correct range for the width should be 10 ≤ width ≤ 14, which doesn't match any of the provided options and suggests there may be a typo.

Step-by-step explanation:

To find the range of values for the width of Dave's workshop, we need to use the area formula of a rectangle, which is length × width. Since the length is fixed at 9 feet, we have the equation 9 × width = area. As we are given that the area should be between 90 and 126 square feet, we set up the compound inequality 90 ≤ 9 × width ≤ 126. Dividing the entire inequality by 9, we simplify it to 10 ≤ width ≤ 14, which matches option A: 6 ≤ width ≤ 14.

However, there seems to be a typo. Considering that we've just calculated it, the correct option should be 10 ≤ width ≤ 14, not option A. This could be a mistake in the provided options.