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Help Me withma5htr

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
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1 Answer

A mass is rejected if it is more than .36 oz from the target weight of 18.25.  We can rephrase this as "The difference between the actual weight (x) and the target weight (18.25) is greater than .36."  The keyword difference tells us to subtract, so in math terms that come out as:
x - 18.25 > .36
 
However, we have to account for cases in which x is less than .36, in which case we change the order:
18.25 - x > .36
 
The absolute value summarizes these two into a single inequality:
|x - 18.25| > .36
 
Last we simplify each of the two original inequalities.
x - 18.25 > .36
x > 18.61           (add 18.25 to both sides)
 
18.25 - x > .36
-x > -17.89        (subtract 18.25 from both sides)
x < 17.89           (Multiply both sides by -1, and don't forget that multiplying by a negative number reverses the direction of the inequality.)
 
So we see that answer A is the only one that fits the three statements we derived.