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 :

                     4/5-(3*w-11/5)<0 

Step by step solution :

Step  1  :

            11
 Simplify   ——
            5 

Equation at the end of step  1  :

  4           11
  — -  (3w -  ——)  < 0 
  5           5 

Step  2  :

Rewriting the whole as an Equivalent Fraction :

 2.1   Subtracting a fraction from a whole

Rewrite the whole as a fraction using  5  as the denominator :

           3w     3w • 5
     3w =  ——  =  ——————
           1        5   

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 :

 2.2       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:

 3w • 5 - (11)     15w - 11
 —————————————  =  ————————
       5              5    

Equation at the end of step  2  :

  4    (15w - 11)
  — -  ——————————  < 0 
  5        5     

Step  3  :

            4
 Simplify   —
            5

Equation at the end of step  3  :

  4    (15w - 11)
  — -  ——————————  < 0 
  5        5     

Step  4  :

Adding fractions which have a common denominator :

 4.1       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:

 4 - ((15w-11))     15 - 15w
 ——————————————  =  ————————
       5               5    

Step  5  :

Pulling out like terms :

 5.1     Pull out like factors :

   15 - 15w  =   -15 • (w - 1) 

Equation at the end of step  5  :

  -15 • (w - 1)
  —————————————  < 0 
        5      

Step  6  :

 6.1    Multiply both sides by  5 

 6.2    Divide both sides by  -15 

Remember to flip the inequality sign:

Solve Basic Inequality :

 6.3      Add  1  to both sides

             w > 1

Inequality Plot :

 6.4      Inequality plot for

         -3.000 X  + 3.000  >  0

  
 

One solution was found :