Solution - Adding, subtracting and finding the least common multiple

Rearrange:

Rearrange the equation by subtracting what is to the right of the greater than sign from both sides of the inequality :

                     -6*x-17/4-(79/4)<0 

Step by step solution :

Step  1  :

            79
 Simplify   ——
            4 

Equation at the end of step  1  :

          17     79
  (-6x -  ——) -  ——  < 0 
          4      4 

Step  2  :

            17
 Simplify   ——
            4 

Equation at the end of step  2  :

          17     79
  (-6x -  ——) -  ——  < 0 
          4      4 

Step  3  :

Rewriting the whole as an Equivalent Fraction :

 3.1   Subtracting a fraction from a whole

Rewrite the whole as a fraction using  4  as the denominator :

            -6x     -6x • 4
     -6x =  ———  =  ———————
             1         4   

Equivalent fraction : The fraction thus generated looks different but has the same value as the whole

Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator

Adding fractions that have a common denominator :

 3.2       Adding up the two equivalent fractions
Add the two equivalent fractions which now have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

 -6x • 4 - (17)     -24x - 17
 ——————————————  =  —————————
       4                4    

Equation at the end of step  3  :

  (-24x - 17)    79
  ——————————— -  ——  < 0 
       4         4 

Step  4  :

Step  5  :

Pulling out like terms :

 5.1     Pull out like factors :

   -24x - 17  =   -1 • (24x + 17) 

Adding fractions which have a common denominator :

 5.2       Adding fractions which have a common denominator
Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

 (-24x-17) - (79)     -24x - 96
 ————————————————  =  —————————
        4                 4    

Step  6  :

Pulling out like terms :

 6.1     Pull out like factors :

   -24x - 96  =   -24 • (x + 4) 

Equation at the end of step  6  :

  -24 • (x + 4)
  —————————————  < 0 
        4      

Step  7  :

 7.1    Multiply both sides by  4 

 7.2    Divide both sides by  -24 

Remember to flip the inequality sign:

Solve Basic Inequality :

 7.3      Subtract  4  from both sides

            x > -4

Inequality Plot :

 7.4      Inequality plot for

         -6.000 X  - 24.000  >  0

  
 

One solution was found :