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A company manufactures penny number 2 nails that are 1 inch in length. The actual length is allowed to vary by up to \displaystyle \frac{1}{32}321​inch.a) Write and solve an absolute value equation to find the minimum and maximum acceptable nail length. (Use \displaystyle ll as the variable to represent length)b) A penny number 2 nail is 1.05 inches long. Is the nail acceptable? Explain.

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The absolute value equation representing the length of the nail is :

  • [tex]\frac{31}{32} \leqslant x \leqslant 1 \frac{1}{32} [/tex]

A nail of length 1.05 inches is unacceptable

Actual Length of nail = 1 inch

Allowable variation = 1/32 inches

The minimum allowable length :

actual length - allowable variation

  • [tex]1 - \frac{1}{32} = \frac{31}{32} [/tex]

The maximum allowable length :

Actual length + allowable variation

  • [tex] 1 + \frac{1}{32} = 1 \frac{1}{32} [/tex]

The length of X, of the nail must be follow the equation :

Minimum ≤ X ≤ maximum

[tex] \frac{31}{32} \leqslant x \leqslant 1 \frac{1}{32} [/tex]

A nail of length 1.05 inches

Maximum nail length = 1 1/32 = 1.031

1.05 > 1.031 ; hence, it is greater than the maximum allowable length and hence, Unacceptabe

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