# Math

posted by .

Solve each inequality algebraically.

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

• Math -

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

## Similar Questions

1. ### Algebra 2(check) cont..

1)solve the inequality -3(r-11)+15>_9 my answer = r<_13 2)solve the inequality -2<4z+10<_12 my answer = -3<z<_1/2 3)solve the inequality 2x-5<_10 or 33-4x<5 my answer is x<_15/2 or <7 4)solve the inequality …
2. ### Math

Solve the inequality. -(x-1)>2(x+1/2) I don't understand how the answer is 0.
3. ### algebra

Solve the inequality algebraically. Graph your solution on a number line.
4. ### math-logic(shsat)

Question: If 15 - 2x < 7, then for all possible values of x that make the inequality true, (a) x<8 (b) x>8 (c) x>4 (d) x<4 (e) x>1/4 Answer: i chose the answer (d) but the answer of the book said (c). i understand …
5. ### college algebra

Solve the inequality algebraically 11x-3¡Ý-4x^2
6. ### college algebra

solve the inequality algebraically 11x-3 is greater than or equal to - 4x^2
7. ### Algebra

Solve each inequality algebraically:how do I solve this problem?
8. ### Solve the inequality

Solve the inequality algebraically 8x-3 ≥ -3x^2
9. ### math

solve the inequality -5(x-7)<15 algebraically for x -5(x-7)<15 -5x+35<15 -35 -35 -5x,-25 -5 -5 divide both sides by -5 x=5 is this correct?