The inequality is 12 <= 3(2+ 1) <= 36, and the length of the rectangle can be between 4 and 12 units.
Here's how to solve for the possible values of x:
Define the variables: Let x be the length of the rectangle. We are given that the width is 3 units.
Express the area as an inequality: We are given that the area A of the rectangle is between 12 and 36 square units.
We can express this as an inequality:
12 <= A <= 36
Substitute the formula for the area: The area of a rectangle is the product of its length and width.
Therefore, we can substitute the formula A = lx into the inequality:
12 <= 3x <= 36
Solve the inequality: Divide all sides by 3 to isolate x:
4 <= x <= 12Therefore, the possible values of x are between 4 and 12 units.
Checking the answer choices:
12 <= 3(2+ 1) <= 36: This is correct. Substituting x = 2 into the inequality, we get 12 <= 9 <= 36, which is true.
Therefore, the correct answer is 12 <= 3(2+ 1) <= 36, and the length of the rectangle can be between 4 and 12 units.
Additional notes:
The values of x are all viable in this situation.
There are no restrictions on the length of the rectangle as long as it falls within the given range of area.
It is important to pay attention to the units when working with inequalities.
In this case, the units are square units for the area and units for the length.