Question

The area of the rectangle shown is described with the inequality 20 ≤ a ≤ 80. If the rectangle has a length of 6x and a width of 2/3, select the compound inequality for the area written in terms of x.

1) 20 ≤ 12x ≤ 80
2) 20 ≤ 9x ≤ 80
3) 20 ≤ 6x ≤ 80
4) 20 ≤ 4x ≤ 80

Answer 1

The compound inequality for the area of the rectangle in terms of x is 20 ≤ 4x ≤ 80.

Step-by-step explanation:

The area of a rectangle is found by multiplying its length and width. In this case, the length is given as 6x and the width is given as 2/3. To find the compound inequality for the area, we need to multiply the length and width and compare it to the given inequality 20 ≤ a ≤ 80.

The area of the rectangle is given by a = (6x)(2/3) = 4x. So, the compound inequality for the area in terms of x is 20 ≤ 4x ≤ 80.