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MANUFACTURING A hardware store sells bags of rock salt that are labeled as weighing 35 pounds.
The equipment used to package the salt produces bags with a weight that is within 8 ounces of the label weight.
Write an absolute value equation to determine the maximum and minimum weights
for the bag of rock salt. Let x represent the weight of the bag, in pounds.
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The question in the problem is posed INCORRECTLY.
The correct question should ask about an absolute value INEQUALITY - - - not about an absolute value equation.
8 ounces = 0.5 of a pound.
An absolute value inequality for this problem is
|x - 35| <= 0.5.
It is the ANSWER to the first question.
This absolute value inequality is equivalent to this compounded inequality
-0.5 <= x - 35 <= 0.5
Add 35 to all three terms of the inequality and get the solution
34.5 <= x <= 35.5.
34.5 pounds and 35.5 pounds are the minimum and the maximum of the weight in a bag.
It is the ANSWER to the second question.
Solved completely.
This my solution is a standard mathematical mantra
to pronounce when solving such problems.
Use it to solve million other similar problems.