Question

A company did a quality check on all the packs of nuts it manufactured. Each pack of nuts is targeted to weigh 18.25 oz. A pack must weigh within 0.36 oz of the target weight to be accepted. What is the range of rejected masses, x, for the manufactured nuts.

x < 17.89 or x > 18.61 because |x – 18.25| > 0.36

x < 17.89 or x > 18.61 because |x – 0.36| + 18.25 > 0

x < 18.25 or x > 18.61 because |x – 18.25| > 0.36

x < 18.25 or x > 18.61 because |x – 0.36| + 18.25 > 0

Answer 1

The question is asking to choose among the following choices that states the range of rejected masses, X, for the manufactured nuts, and base on the given and further computation about the said problem, I would say that the answer among the following is x < 17.89 or x > 18.61 because |x – 18.25| > 0.36

Answer 2

The correct answer is:

x < 17.89 or x > 18.61 because |x – 18.25| > 0.36 .

Step-by-step explanation:

We know that the target weight is 18.25. We also know that to be accepted, the weight of each pack must be within 0.36 of this target weight. The packs can be up to 0.36 more than or up to 0.36 less than the target weight; for this reason, we use an absolute value equation:

|x-18.25| ≤ 0.36

However, we are concerned with the weights of the packs that are rejected. These will be more than 0.36 different from the target weight:

|x-18.25| > 0.36

To solve this, we consider the positive and negative values of 0.36 (since it is an absolute value equation). Remember the rules of inequalities; when we change the sign of the answer, we change the inequality sign as well:

x - 18.25 > 0.36 or x - 18.25 < -0.36

To solve each of these, add 18.25 to each side:

x - 18.25 + 18.25 > 0.36 + 18.25 or x - 18.25 + 18.25 < -0.36 + 18.25

x > 18.61 or x < 17.89

This means the correct choice is the first one.