Solve the inequality.
2|2/5x+3|>3/5

Absolute Value Inequality entered :

     2-|2/5x+3|<3/5

Step by step solution :

STEP

1

:

Rearrange this Absolute Value Inequality

Absolute value inequalitiy entered

     -|2x/5+3|+2 < (3/5)

Another term is moved / added to the right hand side.

To make the absolute value term positive, both sides are multiplied by (-1). This involves switching the direction of the inequality.

     |2x/5+3| > (7/5)

STEP

2

:

Clear the Absolute Value Bars

Clear the absolute-value bars by splitting the equation into its two cases, one for the Positive case and the other for the Negative case.

The Absolute Value term is |2x/5+3|

For the Negative case we'll use -(2x/5+3)

For the Positive case we'll use (2x/5+3)

STEP

3

:

Solve the Negative Case

     -(2x/5+3) > (7/5)

    Multiply

     -2x/5-3 > (7/5)

    Rearrange and Add up

     -2x/5 > (22/5)

    Multiply both sides by 5

     -2x > 22

    Divide both sides by 2

     -x > 11

    Multiply both sides by (-1)

    Remember to flip the inequality sign

     x < -11

    Which is the solution for the Negative Case

STEP

4

:

Solve the Positive Case

     (2x/5+3) > (7/5)

    Rearrange and Add up

     2x/5 > -(8/5)

    Multiply both sides by 5

     2x > -8

    Divide both sides by 2

     x > -4

    Which is the solution for the Positive Case

STEP

5

:

Wrap up the solution

 x < -11

 x > -4

Solutions in Interval Notation

   (-∞,-11)

   (-4,+∞)

Step-by-step explanation:

x < − 33 4  or  x > − 27/4