Solve the inequality and sketch the graph of the solution on the real number line.
|x - a|< or equal to b, b > 0
Let us imagine that the ">" and "<" signs also include "equal to" except for the condition, b > 0, in order to solve this question.
The Attempt at a Solution
My attempt in accordance with the solution that is within the textbook:
|x - a|< b
-b < x - a < b
a - b < x < a + b
Now this is confusing due to the fact that the condition, "b must be greater than 0", prohibits b from being negative in the second line of my attempt. Though this is the only way I know how to solve it. Can anyone explain as to why this is the case? Does the condition just deal with the real number line and placing these values in the positive direction and to the right of zero?