Solution - Adding, subtracting and finding the least common multiple

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "5.8" was replaced by "(58/10)". 4 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 :

           (37/10)*x+(62/10)-(-(73/10)*x-(58/10))=0 

Step by step solution :

Step  1  :

            29
 Simplify   ——
            5 

Equation at the end of step  1  :

    37    62       73     29
  ((——•x)+——)-((0-(——•x))-——)  = 0 
    10    10       10     5 

Step  2  :

            73
 Simplify   ——
            10

Equation at the end of step  2  :

    37    62       73     29
  ((——•x)+——)-((0-(——•x))-——)  = 0 
    10    10       10     5 

Step  3  :

Calculating the Least Common Multiple :

 3.1    Find the Least Common Multiple

      The left denominator is :       10 

      The right denominator is :       5 

      Least Common Multiple:
      10 

Calculating Multipliers :

 3.2    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 = 1

   Right_M = L.C.M / R_Deno = 2

Making Equivalent Fractions :

 3.3      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.      -73x
   ——————————————————  =   ————
         L.C.M              10 

   R. Mult. • R. Num.      29 • 2
   ——————————————————  =   ——————
         L.C.M               10  

Adding fractions that have a common denominator :

 3.4       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:

 -73x - (29 • 2)     -73x - 58
 ———————————————  =  —————————
       10               10    

Equation at the end of step  3  :

    37         62     (-73x - 58)
  ((—— • x) +  ——) -  ———————————  = 0 
    10         10         10     

Step  4  :

            31
 Simplify   ——
            5 

Equation at the end of step  4  :

    37         31     (-73x - 58)
  ((—— • x) +  ——) -  ———————————  = 0 
    10         5          10     

Step  5  :

            37
 Simplify   ——
            10

Equation at the end of step  5  :

    37         31     (-73x - 58)
  ((—— • x) +  ——) -  ———————————  = 0 
    10         5          10     

Step  6  :

Calculating the Least Common Multiple :

 6.1    Find the Least Common Multiple

      The left denominator is :       10 

      The right denominator is :       5 

      Least Common Multiple:
      10 

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 = 1

   Right_M = L.C.M / R_Deno = 2

Making Equivalent Fractions :

 6.3      Rewrite the two fractions into equivalent fractions

   L. Mult. • L. Num.      37x
   ——————————————————  =   ———
         L.C.M             10 

   R. Mult. • R. Num.      31 • 2
   ——————————————————  =   ——————
         L.C.M               10  

Adding fractions that have a common denominator :

 6.4       Adding up the two equivalent fractions

 37x + 31 • 2     37x + 62
 ————————————  =  ————————
      10             10   

Equation at the end of step  6  :

  (37x + 62)    (-73x - 58)
  —————————— -  ———————————  = 0 
      10            10     

Step  7  :

Step  8  :

Pulling out like terms :

 8.1     Pull out like factors :

   -73x - 58  =   -1 • (73x + 58) 

Adding fractions which have a common denominator :

 8.2       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:

 (37x+62) - ((-73x-58))     110x + 120
 ——————————————————————  =  ——————————
           10                   10    

Step  9  :

Pulling out like terms :

 9.1     Pull out like factors :

   110x + 120  =   10 • (11x + 12) 

Equation at the end of step  9  :

  11x + 12  = 0 

Step  10  :

Solving a Single Variable Equation :

 10.1      Solve  :    11x+12 = 0 

 Subtract  12  from both sides of the equation : 
                      11x = -12
Divide both sides of the equation by 11:
                     x = -12/11 = -1.091

One solution was found :