Question

Possible values for the area A of the rectangle shown are 12 ≤ A ≤ 36. Write and solve a compound inequality to find the possible values of x. Are these values all viable in this situation?

Rectangle with width of 2x+1 and length of 3

≤ x ≤

the lengths can be between
and
units.

Answer 1

Do you know what the answer to

Length can be between _____ and _____ units?

Answer 2

Answer: 1.5 ≤ x ≤ 5.5

Explanation:

If the width is W and the length is L, the area of the rectangle will be:

A = W*L

In this case:

W = 2*x + 1

L = 3.

Then the area is:

A = (2*x + 1)*3 = 6*x + 3.

And we know that:

12 ≤ A ≤ 36

To find the smallest possible value of x, we assume that we have the smallest possible area: 12.

A = 12 = 6*x + 3

12 - 3 = 6*x

9/6 = x = 1.5

To find the largest possible value of x, we use the largest possible area, 36.

A = 36 = 6*x + 3.

36 - 3 = 6*x

33/6 = x = 5.5

Then we have:

1.5 ≤ x ≤ 5.5