Question

You are purchasing a new refrigerator. To fit in the space, the width of the refrigerator cannot be more than 42 inches. To meet your storage requirements, the width of the refrigerator must be at least 36 inches. Write a compound inequality that represents this range

Answer 1

Given:

To fit in the space, the width of the refrigerator cannot be more than 42 inches.

To meet your storage requirements, the width of the refrigerator must be at least 36 inches.

To find:

The compound inequality that represents this range.

Solution:

Let w be the width of the refrigerator.

To fit in the space, the width of the refrigerator cannot be more than 42 inches.  It means width of the refrigerator must be less than or equal to 42.

$w\leq 42$         ...(i)

To meet your storage requirements, the width of the refrigerator must be at least 36 inches. It means width of the refrigerator must be greater than or equal to 36.

$w\geq 36$          ...(ii)

Using (i) and (ii), we get

$36\leq w\leq 42$

Therefore, the required compound inequality is $36\leq w\leq 42$.