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An engine piston has a diameter of 9.2 cm, with a tolerance of 0.01 cm. Which absolute value inequality represents the range of values for the diameter of the piston?

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gimmemesomeanswers

for this question, the tolerance is telling us that the actual diameter of the engine is no more than 9.2 + 0.01 cm and now less than 9.2 - 0.01 cm.

Thus the range of values of the actual diameter is

9.19 cm - 9.21 cm

Another way of phrasing this is letting 'x' denote the actual value of the diameter and then limiting 'x' to being within 0.01 cm of 9.2:

|x - 9.2| <= 0.01

Which is identical to

-0.01 <= x - 9.2 <= 0.01

Or . . .

9.19 <= x <= 9.21

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