Solution - Absolute value inequalities

Absolute Value Inequality entered :

      |6-5x|+2≥7 

Step by step solution :

Step  1  :

Rearrange this Absolute Value Inequality

Absolute value inequalitiy entered
      |-5x+6|+2 ≥ 7 

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

      |-5x+6| ≥ 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 |-5x+6|

 For the Negative case we'll use -(-5x+6) 

For the Positive case we'll use (-5x+6) 

Step  3  :

Solve the Negative Case

      -(-5x+6) ≥ 5 

     Multiply
      5x-6 ≥ 5 

     Rearrange and Add up
      5x ≥ 11 

     Divide both sides by 5
      x ≥ (11/5) 

Step  4  :

Solve the Positive Case

      (-5x+6) ≥ 5 

     Rearrange and Add up
      -5x ≥ -1 

     Divide both sides by 5
      -x ≥ -(1/5) 

     Multiply both sides by (-1)
     Remember to flip the inequality sign
      x ≤ (1/5) 
     Which is the solution for the Positive Case

Step  5  :

Wrap up the solution

  x ≤ 1/5
  x ≥ 11/5

Solutions in Interval Notation

    (-∞,1/5]
 
    [11/5,+∞) 

Solutions on the Number Line

Two solutions were found :

1.   x ≥ 11/5
2.   x ≤ 1/5