Posted by **Madison** on Monday, August 30, 2010 at 2:52pm.

Solve each inequality algebraically.

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

- Math -
**MathMate**, Monday, August 30, 2010 at 3:11pm
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) **<**-4

x<-3

Apply the same way to the given inequation and you should arrive at

-2<x<3 as the answer.

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