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?
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
