Solution - Absolute value inequalities

Absolute Value Inequality entered :

      |2x-5|+3x≤4x-1 

Step by step solution :

Step  1  :

Rearrange this Absolute Value Inequality

Absolute value inequalitiy entered
      |2x-5|+3x ≤ 4x-1 

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

      |2x-5| ≤ x-1 

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|

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

For the Positive case we'll use (2x-5) 

Step  3  :

Solve the Negative Case

      -(2x-5) ≤ x-1 

     Multiply
      -2x+5 ≤ x-1 

     Rearrange and Add up
      -3x ≤ -6 

     Divide both sides by 3
      -x ≤ -2 

     Multiply both sides by (-1)
     Remember to flip the inequality sign
      x ≥ 2 
     Which is the solution for the Negative Case

Step  4  :

Solve the Positive Case

      (2x-5) ≤ x-1 

     Rearrange and Add up
      x ≤ 4 

     Which is the solution for the Positive Case

Step  5  :

Wrap up the solution

    2 ≤ x ≤ 4

Solution in Interval Notation

    [2,4] 

Solution on the Number Line

One solution was found :