Question

A company manufactures penny number 2 nails that are 1 inch in length. The actual length is allowed to vary by up to 1/32 inch.a. Write and solve an absolute value equation to find the minimum and maximum acceptable nail length.b. A penny number 2 nail is 1.05 inches long. Is the nail acceptable? Explain.

Answer 1

'L' is the lenght that each nail should have. 'x' is the actual length of a nail. The difference between these two values must be under 1/32 inch.

The equation for this is:

`\mleft|x-L\mright|<(1)/(32)`

Since L = 1in, this is:

`\mleft|x-1\mright|<(1)/(32)`

b. If x = 1.05in, to check if it's length is acceptable you have to replce x in the equation above and solve:

`\mleft|1.05-1\mright|<(1)/(32)`
`\mleft|0.05\mright|<(1)/(32)`
`0.05<0.03125`

This inequality is false because 0.05 is not less than 0.031. So the answer is no, the length of this nail is not acceptable.