An absolute value equation to find the minimum and maximum acceptable nail length is; 31/32 ≤ X ≤ 1 ¹/₃₂
How to solve absolute value functions?
We are told that the company manufactures 2 nails that are 1 inch in length. The actual length is allowed to vary by up to 1/32 inch. Thus;
Actual Length of nail = 1 inch
Allowable variation = 1/32 inches
The minimum allowable length is expressed as:
minimum allowable length = actual length - allowable variation
minimum allowable length = 1 - (1/32) = 31/32
The maximum allowable length is expressed as:
Maximum allowable length = Actual length + allowable variation
Maximum allowable length = 1 + (1/32) = 1 ¹/₃₂
The length of X, of the nail must be follow the equation :
Minimum ≤ X ≤ maximum
Thus, an absolute value equation to find the minimum and maximum acceptable nail length is; 31/32 ≤ X ≤ 1 ¹/₃₂
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