Answer
(a) $|x-0.020|\leq 0.003$
(b) $0.017\leq x \leq 0.023$
Work Step by Step
Let $x$ be actual thickness of the sheet.
(a) The difference between the thickness of sheet that the factory has to provide and actual thickness is $0.003in$. Which could be more (positive) or less (negative) :
$x-0.020\leq 0.003$
But, thickness cannot be negative, so to find the difference we have to involve absolute value:
$|x-0.020|\leq 0.003$
(b) To solve the inequality, we have to consider two possible value of the left-hand side (the absolute value), that is negative and positive.
If positive:
$x-0.020 \leq 0.003$
$x\leq 0.023$
If negative:
$-(x-0.020)\leq 0.003$
$-x+0.020\leq 0.003$
$x\geq0.017$
So, we have the interval:
$0.017\leq x \leq 0.023$
