Answer
The range of acceptable lengths of the nail is between 19.6mm and 20.4mm.
Work Step by Step
The ideal length of a certain nail is 20 mm: $|x-20|$
The actual length can vary from the ideal length by at most 0.4 mm.
Thus: $|x-20| \leq 0.4$
$-0.4 \leq x -20 \leq 0.4$
$19.6 \leq x \leq 20.4$
The range of acceptable lengths of the nail is between 19.6mm and 20.4mm.
