Question

A company did a quality check on all the packs of trail mix it manufactured. Each pack of trail mix is targeted to weigh 9.25 oz. A pack must weigh within 0.23 oz of the target weight to be accepted. Find the absolute value inequality that describes the situation and solve it to find the range of rejected masses, x.
|x − 0.23| + 9.25 > 0; x < 9.02 or x > 9.48
|x − 9.25| > 0.23; x < 9.25 or x > 9.48
|x − 0.23| + 9.25 > 0; x < 9.25 or x > 9.48
|x − 9.25| > 0.23; x < 9.02 or x > 9.48

Answer 1

Each pack of trail mix is targeted to weigh 9.25 oz.

A pack must weigh within 0.23 oz of the target weight to be accepted.

Let the weight of the pack x

The range of accepted weight will be as following:

∴ 9.25 - 0.23 < x < 9.25 + 0.23  

subtract 9.25 from all sides

∴ -0.23 < x - 9.25 < 0.23

which can be written as ⇒⇒⇒  | x - 9.25 | < 0.23

So, the rejected weight is the inverse of that inequality.

∴ The absolute value inequality for the rejected weight range is:

| x - 9.25 | > 0.23

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So, the range of rejected masses:    x < 9.02   OR  x > 9.48