Solution - Adding, subtracting and finding the least common multiple

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "0.296" was replaced by "(296/1000)". 3 more similar replacement(s)

Rearrange:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

           -(133/10)+k/(11796/1000)-(-(296/1000))=0 

Step by step solution :

Step  1  :

             37
 Simplify   ———
            125

Equation at the end of step  1  :

      133  11796      37
  ((0-———)+—————)-(0-———)  = 0 
      10   1000      125

Step  2  :

            2949
 Simplify   ————
            250 

Equation at the end of step  2  :

         133     2949     -37
  ((0 -  ———) +  ————) -  ———  = 0 
         10      250      125

Step  3  :

                2949
 Divide  k  by  ————
                250 

Equation at the end of step  3  :

         133     250k     -37
  ((0 -  ———) +  ————) -  ———  = 0 
         10      2949     125

Step  4  :

            133
 Simplify   ———
            10 

Equation at the end of step  4  :

         133     250k     -37
  ((0 -  ———) +  ————) -  ———  = 0 
         10      2949     125

Step  5  :

Calculating the Least Common Multiple :

 5.1    Find the Least Common Multiple

      The left denominator is :       10 

      The right denominator is :       2949 

      Least Common Multiple:
      29490 

Calculating Multipliers :

 5.2    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 = 2949

   Right_M = L.C.M / R_Deno = 10

Making Equivalent Fractions :

 5.3      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.      -133 • 2949
   ——————————————————  =   ———————————
         L.C.M                29490   

   R. Mult. • R. Num.      250k • 10
   ——————————————————  =   —————————
         L.C.M               29490  

Adding fractions that have a common denominator :

 5.4       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:

 -133 • 2949 + 250k • 10     2500k - 392217
 ———————————————————————  =  ——————————————
          29490                  29490     

Equation at the end of step  5  :

  (2500k - 392217)    -37
  ———————————————— -  ———  = 0 
       29490          125

Step  6  :

Calculating the Least Common Multiple :

 6.1    Find the Least Common Multiple

      The left denominator is :       29490 

      The right denominator is :       125 

      Least Common Multiple:
      737250 

Calculating Multipliers :

 6.2    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 = 25

   Right_M = L.C.M / R_Deno = 5898

Making Equivalent Fractions :

 6.3      Rewrite the two fractions into equivalent fractions

   L. Mult. • L. Num.      (2500k-392217) • 25
   ——————————————————  =   ———————————————————
         L.C.M                   737250       

   R. Mult. • R. Num.      -37 • 5898
   ——————————————————  =   ——————————
         L.C.M               737250  

Adding fractions that have a common denominator :

 6.4       Adding up the two equivalent fractions

 (2500k-392217) • 25 - (-37 • 5898)     62500k - 9587199
 ——————————————————————————————————  =  ————————————————
               737250                        737250     

Equation at the end of step  6  :

  62500k - 9587199
  ————————————————  = 0 
       737250     

Step  7  :

When a fraction equals zero :

 7.1    When a fraction equals zero ...

Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.

Now,to get rid of the denominator, Tiger multiplys both sides of the equation by the denominator.

Here's how:

  62500k-9587199
  —————————————— • 737250 = 0 • 737250
      737250    

Now, on the left hand side, the  737250  cancels out the denominator, while, on the right hand side, zero times anything is still zero.

The equation now takes the shape :
   62500k-9587199  = 0

Solving a Single Variable Equation :

 7.2      Solve  :    62500k-9587199 = 0 

 Add  9587199  to both sides of the equation : 
                      62500k = 9587199
Divide both sides of the equation by 62500:
                     k = 9587199/62500 = 153.395

One solution was found :