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 :

                     2/7*f-14-(20-5/7*f)<0 

Step by step solution :

Step  1  :

            5
 Simplify   —
            7

Equation at the end of step  1  :

    2             5
  ((—•f)-14)-(20-(—•f))  < 0 
    7             7

Step  2  :

Rewriting the whole as an Equivalent Fraction :

 2.1   Subtracting a fraction from a whole

Rewrite the whole as a fraction using  7  as the denominator :

           20     20 • 7
     20 =  ——  =  ——————
           1        7   

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:

 20 • 7 - (5f)     140 - 5f
 —————————————  =  ————————
       7              7    

Equation at the end of step  2  :

    2                (140 - 5f)
  ((— • f) -  14) -  ——————————  < 0 
    7                    7     

Step  3  :

            2
 Simplify   —
            7

Equation at the end of step  3  :

    2                (140 - 5f)
  ((— • f) -  14) -  ——————————  < 0 
    7                    7     

Step  4  :

Rewriting the whole as an Equivalent Fraction :

 4.1   Subtracting a whole from a fraction

Rewrite the whole as a fraction using  7  as the denominator :

          14     14 • 7
    14 =  ——  =  ——————
          1        7   

Adding fractions that have a common denominator :

 4.2       Adding up the two equivalent fractions

 2f - (14 • 7)     2f - 98
 —————————————  =  ———————
       7              7   

Equation at the end of step  4  :

  (2f - 98)    (140 - 5f)
  ————————— -  ——————————  < 0 
      7            7     

Step  5  :

Step  6  :

Pulling out like terms :

 6.1     Pull out like factors :

   2f - 98  =   2 • (f - 49) 

Step  7  :

Pulling out like terms :

 7.1     Pull out like factors :

   140 - 5f  =   -5 • (f - 28) 

Adding fractions which have a common denominator :

 7.2       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:

 2 • (f-49) - (-5 • (f-28))     7f - 238
 ——————————————————————————  =  ————————
             7                     7    

Step  8  :

Pulling out like terms :

 8.1     Pull out like factors :

   7f - 238  =   7 • (f - 34) 

Equation at the end of step  8  :

  f - 34  < 0 

Step  9  :

Solve Basic Inequality :

 9.1      Add  34  to both sides

             f < 34

Inequality Plot :

 9.2      Inequality plot for

         f  - 34.000  <  0

  
 

One solution was found :