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 :

                     37/8*c+339/40-(155/5)>0 

Step by step solution :

Step  1  :

            31
 Simplify   ——
            1 

Equation at the end of step  1  :

    37         339     
  ((—— • c) +  ———) -  31  > 0 
    8          40      

Step  2  :

            339
 Simplify   ———
            40 

Equation at the end of step  2  :

    37         339     
  ((—— • c) +  ———) -  31  > 0 
    8          40      

Step  3  :

            37
 Simplify   ——
            8 

Equation at the end of step  3  :

    37         339     
  ((—— • c) +  ———) -  31  > 0 
    8          40      

Step  4  :

Calculating the Least Common Multiple :

 4.1    Find the Least Common Multiple

      The left denominator is :       8 

      The right denominator is :       40 

      Least Common Multiple:
      40 

Calculating Multipliers :

 4.2    Calculate multipliers for the two fractions


    Denote the Least Common Multiple by  L.C.M 
    Denote the Left Multiplier by  Left_M 
    Denote the Right Multiplier by  Right_M 
    Denote the Left Deniminator by  L_Deno 
    Denote the Right Multiplier by  R_Deno 

   Left_M = L.C.M / L_Deno = 5

   Right_M = L.C.M / R_Deno = 1

Making Equivalent Fractions :

 4.3      Rewrite the two fractions into equivalent fractions

Two fractions are called equivalent if they have the same numeric value.

For example :  1/2   and  2/4  are equivalent,  y/(y+1)²   and  (y²+y)/(y+1)³  are equivalent as well.

To calculate equivalent fraction , multiply the Numerator of each fraction, by its respective Multiplier.

   L. Mult. • L. Num.      37c • 5
   ——————————————————  =   ———————
         L.C.M               40   

   R. Mult. • R. Num.      339
   ——————————————————  =   ———
         L.C.M             40 

Adding fractions that have a common denominator :

 4.4       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:

 37c • 5 + 339     185c + 339
 —————————————  =  ——————————
      40               40    

Equation at the end of step  4  :

  (185c + 339)    
  ———————————— -  31  > 0 
       40         

Step  5  :

Rewriting the whole as an Equivalent Fraction :

 5.1   Subtracting a whole from a fraction

Rewrite the whole as a fraction using  40  as the denominator :

          31     31 • 40
    31 =  ——  =  ———————
          1        40   

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 :

 5.2       Adding up the two equivalent fractions

 (185c+339) - (31 • 40)     185c - 901
 ——————————————————————  =  ——————————
           40                   40    

Equation at the end of step  5  :

  185c - 901
  ——————————  > 0 
      40    

Step  6  :

 6.1    Multiply both sides by  40 

 6.2    Divide both sides by  185  

      c-(901/185)  > 0

Solve Basic Inequality :

 6.3      Add  901/185  to both sides

             c > 901/185

Inequality Plot :

 6.4      Inequality plot for

         4.625 c  - 22.525  >  0

  
 

One solution was found :