Question

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?

Answer 1

You would see this is a problem that asks you to find a domain for which the range is true in, for example, problems involving limits.

|x-a| < b means -b + a < x < b + a and this means x is an element of the open interval (-b + a,b + a)