'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:
[tex]\mleft|x-L\mright|<\frac{1}{32}[/tex]Since L = 1in, this is:
[tex]\mleft|x-1\mright|<\frac{1}{32}[/tex]b. If x = 1.05in, to check if it's length is acceptable you have to replce x in the equation above and solve:
[tex]\mleft|1.05-1\mright|<\frac{1}{32}[/tex][tex]\mleft|0.05\mright|<\frac{1}{32}[/tex][tex]0.05<0.03125[/tex]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.
