the absolute value can be seen as the difference/distance between x and a is less than b.
example:
you are cutting a long log into one-foot pieces. pieces that are within i inches longer or shorter than 1 inch shorter than the standard length 12 inches are still acceptable, what can the actual length of the wood piece be?
in this example, x is the actual length, a is the standard length 12 inches, and b is the difference 1 inch.
