Question

A pencil manufacturer has a certain tolerance for the actual lengths of the pencils it produces. After the pencils are manufactured, a 1.1 centimeter eraser is added to one end of the pencil. The total length of each pencil must be between 12.9 cm and 13.3 cm. Write an inequality representing the possible lengths of the pencils before the erasers have been added, and then find the lengths.

Answer 1

A.
12.9 < |x + 1.1| < 13.3; the pencils must be between 11.8 cm and 12.2 cm.
B.
12.9 < |x + 1.1| < 13.3; the pencils must be between 12.0 cm and 12.2 cm.
C.
1.1 < |x + 12.9| < 13.3; the pencils must be between –11.8 cm and 1.1 cm.
D.
12.9 < |x| < 13.3; the pencils must be between 12.9 cm and 13.3 cm.

Answer 2

If x represents the length of the pencil, then the total length is x + 1.1 cm.

So x + 1.1 must be between 12.9 and 13.3:

12.9 <|x+1.1| < 13.3 is the answer. The absolute values are not necessary.