Question

The area A of the rectangle shown is described with the inequality 100 ≤ A ≤ 1,000. A rectangle with length 4 X and width 5. Select the compound inequality for the area written in terms of x.

A. 100 ≤ 10 + 8x ≤ 1,000
B. 100 ≤ 18x ≤ 1,000
C. 100 ≤ 9x ≤ 1,000
D. 100 ≤ 20x ≤ 1,000

Answer 1

The correct compound inequality for the rectangle's area, given the length as 4x and the width as 5, is D. 100 ≤ 20x ≤ 1,000. This inequality can be simplified by dividing by 20 to get 5 ≤ x ≤ 50.

Step-by-step explanation:

To find the compound inequality for the area of a rectangle in terms of x, we must consider the given area constraints, which are 100 ≤ A ≤ 1,000. The area (A) of a rectangle is the product of its length and width. In our case, the length is 4x and the width is 5, so the area would be A = 4x × 5 = 20x.

Given the inequality that describes the area of the rectangle, the corresponding compound inequality in terms of x would need to reflect the relationship 100 ≤ 20x ≤ 1,000. This inequality can be simplified by dividing all parts by 20 to isolate x, resulting in 5 ≤ x ≤ 50.

Therefore, the correct option is D. 100 ≤ 20x ≤ 1,000. This represents the compound inequality for the rectangle's area written in terms of x.