Acircular lid is being designed for a container. The diameter d of the lid is to be 3.6 inches and must be accurate to within 0.07 inch White an absolute value inequality that gives acceptable values for d. The absolute value inequality is square (Type an inequality.)

## Step 1<br />The problem involves the concept of absolute value inequalities. The absolute value of a number is its distance from zero on the number line, regardless of direction. In this case, the diameter of the lid, \(d\), is to be 3.6 inches, but it must be 0.07 inch. This means that the diameter can vary by 0.07 inch from the target value of 3.6 inches.<br /><br />## Step 2<br />The absolute value inequality that represents this situation is \(|d - 3.6| \leq 0.07\). This inequality states that the difference between the actual diameter and the target diameter (3.6 inches) must be less than or equal to 0.07 inch.<br /><br />## Step 3<br />This inequality can be interpreted as the diameter being within 0.07 inch of 3.6 inches. This means that the diameter can be as small as \(3.6 - 0.07 = 3.53\) inches or as large as \(3.6 + 0.07 = 3.67\) inches.