Question

A piece of material for one article of clothing must be within 0.5 cm of 15 cm in width. Write and solve an inequality that allows a clothing designer to determine the range of widths, from shortest to longest, that the material may measure.

A) 14.5 cm ≤ x ≤ 15.5 cm
B) 14.5 cm < x < 15.5 cm
C) 14.5 cm > x > 15.5 cm
D) x ≤ 14.5 cm or x ≥ 15.5 cm

Answer 1

The correct inequality to represent the allowable range of widths for the material is 14.5 cm ≤ x ≤ 15.5 cm, which ensures the material is within 0.5 cm of the target width of 15 cm.

Step-by-step explanation:

The question is asking to write an inequality that represents the allowable range of widths for a piece of material that needs to be within 0.5 cm of 15 cm. This means that the material can be 0.5 cm less than or greater than 15 cm. Thus, the inequality we are looking for is:

14.5 cm ≤ x ≤ 15.5 cm

This indicates that the width of the material, represented by x, must be greater than or equal to 14.5 cm and less than or equal to 15.5 cm. To solve this inequality, you essentially check if a given measurement falls within this range.