Solution - Adding, subtracting and finding the least common multiple

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "2.2" was replaced by "(22/10)". 2 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 :

           -x-((68/10)*x-4*((22/10)*x-6)-10)=0 

Step by step solution :

Step  1  :

            11
 Simplify   ——
            5 

Equation at the end of step  1  :

        68         11
  -x-(((——•x)-(4•((——•x)-6)))-10)  = 0 
        10         5 

Step  2  :

Rewriting the whole as an Equivalent Fraction :

 2.1   Subtracting a whole from a fraction

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

         6     6 • 5
    6 =  —  =  —————
         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 :

 2.2       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:

 11x - (6 • 5)     11x - 30
 —————————————  =  ————————
       5              5    

Equation at the end of step  2  :

        68       (11x-30)
  -x-(((——•x)-(4•————————))-10)  = 0 
        10          5    

Step  3  :

Equation at the end of step  3  :

        68    4•(11x-30)
  -x-(((——•x)-——————————)-10)  = 0 
        10        5     

Step  4  :

            34
 Simplify   ——
            5 

Equation at the end of step  4  :

           34         4 • (11x - 30)     
  -x -  (((—— • x) -  ——————————————) -  10)  = 0 
           5                5            

Step  5  :

Adding fractions which have a common denominator :

 5.1       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:

 34x - (4 • (11x-30))     120 - 10x
 ————————————————————  =  —————————
          5                   5    

Equation at the end of step  5  :

         (120 - 10x)    
  -x -  (——————————— -  10)  = 0 
              5         

Step  6  :

Rewriting the whole as an Equivalent Fraction :

 6.1   Subtracting a whole from a fraction

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

          10     10 • 5
    10 =  ——  =  ——————
          1        5   

Step  7  :

Pulling out like terms :

 7.1     Pull out like factors :

   120 - 10x  =   -10 • (x - 12) 

Adding fractions that have a common denominator :

 7.2       Adding up the two equivalent fractions

 -2 • (x-12) - (10)     14 - 2x
 ——————————————————  =  ———————
         1                 1   

Equation at the end of step  7  :

        (14 - 2x)
  -x -  —————————  = 0 
            1    

Step  8  :

Equation at the end of step  8  :

  x - 14  = 0 

Step  9  :

Solving a Single Variable Equation :

 9.1      Solve  :    x-14 = 0 

 Add  14  to both sides of the equation : 
                      x = 14

One solution was found :