Question

Solve each inequality algebraically.

|2x-1|-2<3 I don't understand how the answer is -2<x<3

Answer 1

There are two important points involved:
1. When an inequality is multiplied or divided by a negative number on each side, the inequality changes direction.
For example:
4<5
-4>-5

2. When the absolute function comes into play, we have two conditions which have to be considered separately:
a. the contents of the absolute function is positive, and
b. the content of the absolute function is negative.
This means we double the number of conditions.
For example, to solve
|x-1|>4
we have
a. x-1>4, => x>5, and
b. -(x-1) > 4, therefore
(x-1) <b><</b>-4
x<-3

Apply the same way to the given inequation and you should arrive at
-2<x<3 as the answer.