A company did a quality check on all the packs of roasted almonds it manufactured. Each pack of roasted almonds is targeted to weigh 21.25 oz. A pack must weigh within 0.24 oz of the target weight to be accepted. What is the range of rejected masses, x, for the manufactured roasted almonds?

x 21.49 because |x - 0.24| + 21.25 > 0

x 21.49 because |x - 21.25| > 0.24

x 21.49 because |x - 21.25| > 0.24

x 21.49 because |x - 0.24| + 21.25 > 0

The correct answer is:

x 21.49 because |x - 21.25| > 0.24.

Explanation:

Let x be the weight of a given pack of roasted almonds. We know that the difference between x, the actual weight, and the target weight, 21.25, must be no more than 0.24. Since it could be heavier or lighter than the target weight, we use absolute value:

|x-21.25| ≤ 0.24

However, we want to know the weights of the packs that will be rejected. This changes our inequality; now we want the ones that are more than 0.24 different:

|x-21.25| > 0.24

To solve this, we must set up two inequalities (absolute value could mean heavier than or lighter than, we must account for both):

x - 21.25 > 0.24 or x - 21.25 < - 0.24

When we set this up, we change the answer to a negative in the second inequality. Due to the rules of inequalities, when we change the sign of the number, we must change the inequality sign as well. This is why the second inequality has a less than rather than a greater than.

To solve each inequality, we will add 21.25 to each side:

x - 21.25 + 21.25 > 0.24 + 21.25 or x - 21.25 + 21.25 < - 0.24 + 21.25

x > 21.49 or x < 21.01

This makes the correct answer the third option.