Solution - Absolute value inequalities

Absolute Value Inequality entered :

      |7y+5|>0 

Step by step solution :

Step  1  :

Rearrange this Absolute Value Inequality

Absolute value inequalitiy entered
      |7y+5| > 0 

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 |7y+5|

 For the Negative case we'll use -(7y+5) 

For the Positive case we'll use (7y+5) 

Step  3  :

Solve the Negative Case

      -(7y+5) > 0 

     Multiply
      -7y-5 > 0 

     Rearrange and Add up
      -7y > 5 

     Divide both sides by 7
      -y > (5/7) 

     Multiply both sides by (-1)
     Remember to flip the inequality sign
      y < -(5/7) 
     Which is the solution for the Negative Case

Step  4  :

Solve the Positive Case

      (7y+5) > 0 

     Rearrange and Add up
      7y > -5 

     Divide both sides by 7
      y > -(5/7) 

     Which is the solution for the Positive Case

Step  5  :

Wrap up the solution

We found two solutions:
 y  <  -5/7
  
And:   y  >  -5/7
  

  y < -5/7
  y > -5/7

Solutions in Interval Notation

    (-∞,-5/7)
 
    (-5/7,+∞) 

Solutions on the Number Line

Two solutions were found :

1.   y > -5/7
2.   y < -5/7