Describe in words what the absolute value inequality |x - a| < b represents. what phrase might you see in a word problem that would indicate to write this type of inequality?

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. 

101,910,000 people is the answer, good luck