Solution - Adding, subtracting and finding the least common multiple

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "66.3" was replaced by "(663/10)". 2 more similar replacement(s)

Rearrange:

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

                     m-(86/10)-((663/10))>0 

Step by step solution :

Step  1  :

            663
 Simplify   ———
            10 

Equation at the end of step  1  :

        86     663
  (m -  ——) -  ———  > 0 
        10     10 

Step  2  :

            43
 Simplify   ——
            5 

Equation at the end of step  2  :

        43     663
  (m -  ——) -  ———  > 0 
        5      10 

Step  3  :

Rewriting the whole as an Equivalent Fraction :

 3.1   Subtracting a fraction from a whole

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

          m     m • 5
     m =  —  =  —————
          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 :

 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:

 m • 5 - (43)     5m - 43
 ————————————  =  ———————
      5              5   

Equation at the end of step  3  :

  (5m - 43)    663
  ————————— -  ———  > 0 
      5        10 

Step  4  :

Calculating the Least Common Multiple :

 4.1    Find the Least Common Multiple

      The left denominator is :       5 

      The right denominator is :       10 

      Least Common Multiple:
      10 

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 = 2

   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.      (5m-43) • 2
   ——————————————————  =   ———————————
         L.C.M                 10     

   R. Mult. • R. Num.      663
   ——————————————————  =   ———
         L.C.M             10 

Adding fractions that have a common denominator :

 4.4       Adding up the two equivalent fractions

 (5m-43) • 2 - (663)     10m - 749
 ———————————————————  =  —————————
         10                 10    

Equation at the end of step  4  :

  10m - 749
  —————————  > 0 
     10    

Step  5  :

 5.1    Multiply both sides by  10 

 5.2    Divide both sides by  10  

      m-(749/10)  > 0

Solve Basic Inequality :

 5.3      Add  749/10  to both sides

             m > 749/10

Inequality Plot :

 5.4      Inequality plot for

         m  - 74.900  >  0

  
 

One solution was found :