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A company did a quality check on all the packs of trail mixes it manufactured. Each pack of trail mixes is targeted to weigh 9.25 oz. A pack must weigh within 0.23 oz of the target weight to be accepted. What is the range of rejected masses, x, for the manufactured trail mixes?

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If each pack of trail mixes is targeted to weigh 9.25 oz and must be within 0.23 oz of the target in order to be accepted, then rejected masses x, are those which weighs less than 9.02 oz or greater than 9.48 oz. 

Answer: The range of the rejected masses is,

|x-9.25| > 0.23

Step-by-step explanation:

Since, the weight of the pack = 9.25 oz

Also, the maximum changes in the weight = 0.23 oz

Thus, The maximum weight of the pack = 9.25 + 0.23

And, the minimum weight of the pack = 9.25 - 0.23

Thus, the if the weight is more than 9.25 + 0.23 or less than 9.25 - 0.23, then it will be rejected.

If x represents the rejected mass,

Then, 9.25 - 0.23 > x or  9.25 + 0.23 < x

⇒ -0.23 > x - 9.25  or 0.23 < x - 9.25

⇒ 0.23 < -(x-9.25) or 0.23 < x-9.25   ( Since, a > b ⇒ -a < - b )

⇒ 0.23 < | x - 9.25 |

Which is the required range of the rejected mass.

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