Question

Manufacturing A quality control inspector at a bolt factory examines random
bolts that come off the assembly line. Any bolt whose diameter differs by more than
0.04 mm from 6,5 mm is sent back. Write and solve an absolute-value equation to
find the maximum and minimum diameters of an acceptable bolt.

Answer 1

Using absolute value, it is found that:

• The minimum diameter is of 4.46 mm.
• The maximum diameter is of 6.54 mm.

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• The absolute value measures the distance of a point to the origin.

• The diameter is D.
• The difference of D and 6.5 mm should be of at most 0.04 mm, thus, the absolute value inequality is:

$|D - 6.5| \leq 0.04$

Thus:

$-0.04 \leq D - 6.5 \leq 0.04$

The solutions are:

$D - 6.5 \geq -0.04 \rightarrow D \geq 6.46$

$D - 6.5 \leq 0.04 \rightarrow D \leq 6.54$

Which means that:

• The minimum diameter is of 4.46 mm.
• The maximum diameter is of 6.54 mm.

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