Question

introduction to compound inequalities
the weight of a box of cereal can vary by $\frac{1}{4}$ of an ounce and still be sold as a full box. each box is supposed to contain 18 ounces of cereal. which graph represents the possible weights of boxes that are overfilled or underfilled and cannot be sold as full boxes?

Explanation:

Step1: Find acceptable weight range

First, calculate the minimum acceptable weight: $18 - \frac{1}{4} = 17.75$ ounces.
Calculate the maximum acceptable weight: $18 + \frac{1}{4} = 18.25$ ounces.
So boxes that can be sold as full have weights where $17.75 \leq w \leq 18.25$.

Step2: Identify unacceptable weights

Unacceptable weights (cannot be sold as full) are weights less than 17.75 OR greater than 18.25, written as $w < 17.75$ or $w > 18.25$.

Step3: Match to number line graph

On a number line, this means open circles at 17.75 and 18.25 (since these values are still acceptable, so we exclude them from the unacceptable range), with arrows pointing left from 17.75 and right from 18.25.

Answer:

The fourth graph (with open circles at 17.75 and 18.25, and arrows extending left from 17.75 and right from 18.25) represents the possible weights of boxes that cannot be sold as full boxes.