Solution - Adding, subtracting and finding the least common multiple

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "7.7" was replaced by "(77/10)". 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 :

                (34/10)/x-((217/100)/(77/10))=0 

Step by step solution :

Step  1  :

            77
 Simplify   ——
            10

Equation at the end of step  1  :

  34       217   77
  —— ÷ x - ——— ÷ ——  = 0 
  10       100   10

Step  2  :

            217
 Simplify   ———
            100

Equation at the end of step  2  :

  34       217   77
  —— ÷ x - ——— ÷ ——  = 0 
  10       100   10

Step  3  :

         217      77
 Divide  ———  by  ——
         100      10

 3.1    Dividing fractions

To divide fractions, write the divison as multiplication by the reciprocal of the divisor :

217     77       217     10
———  ÷  ——   =   ———  •  ——
100     10       100     77

Equation at the end of step  3  :

  34        31
  —— ÷ x - ———  = 0 
  10       110

Step  4  :

            17
 Simplify   ——
            5 

Equation at the end of step  4  :

  17         31
  —— ÷ x -  ———  = 0 
  5         110

Step  5  :

         17      
 Divide  ——  by  x
         5       

Equation at the end of step  5  :

  17     31
  —— -  ———  = 0 
  5x    110

Step  6  :

Calculating the Least Common Multiple :

 6.1    Find the Least Common Multiple

      The left denominator is :       5x 

      The right denominator is :       110 

      Least Common Multiple:
      110x 

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 = 22

   Right_M = L.C.M / R_Deno = x

Making Equivalent Fractions :

 6.3      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.      17 • 22
   ——————————————————  =   ———————
         L.C.M              110x  

   R. Mult. • R. Num.      31 • x
   ——————————————————  =   ——————
         L.C.M              110x 

Adding fractions that have a common denominator :

 6.4       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:

 17 • 22 - (31 • x)     374 - 31x
 ——————————————————  =  —————————
        110x              110x   

Equation at the end of step  6  :

  374 - 31x
  —————————  = 0 
    110x   

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:

  374-31x
  ——————— • 110x = 0 • 110x
   110x  

Now, on the left hand side, the  110x  cancels out the denominator, while, on the right hand side, zero times anything is still zero.

The equation now takes the shape :
   374-31x  = 0

Solving a Single Variable Equation :

 7.2      Solve  :    -31x+374 = 0 

 Subtract  374  from both sides of the equation : 
                      -31x = -374
Multiply both sides of the equation by (-1) :  31x = 374


Divide both sides of the equation by 31:
                     x = 374/31 = 12.065

One solution was found :