Solution - Adding, subtracting and finding the least common multiple

Rearrange:

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

                     -21/7*n-6/7-(-13/7)=0 

Step by step solution :

Step  1  :

            13
 Simplify   ——
            7 

Equation at the end of step  1  :

       21     6     13
  ((0-(——•n))-—)-(0-——)  = 0 
       7      7     7 

Step  2  :

            6
 Simplify   —
            7

Equation at the end of step  2  :

          21          6     -13
  ((0 -  (—— • n)) -  —) -  ———  = 0 
          7           7      7 

Step  3  :

            3
 Simplify   —
            1

Equation at the end of step  3  :

                     6     -13
  ((0 -  (3 • n)) -  —) -  ———  = 0 
                     7      7 

Step  4  :

Rewriting the whole as an Equivalent Fraction :

 4.1   Subtracting a fraction from a whole

Rewrite the whole as a fraction using  7  as the denominator :

            -3n     -3n • 7
     -3n =  ———  =  ———————
             1         7   

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 :

 4.2       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:

 -3n • 7 - (6)     -21n - 6
 —————————————  =  ————————
       7              7    

Equation at the end of step  4  :

  (-21n - 6)    -13
  —————————— -  ———  = 0 
      7          7 

Step  5  :

Step  6  :

Pulling out like terms :

 6.1     Pull out like factors :

   -21n - 6  =   -3 • (7n + 2) 

Adding fractions which have a common denominator :

 6.2       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:

 -3 • (7n+2) - (-13)     7 - 21n
 ———————————————————  =  ———————
          7                 7   

Step  7  :

Pulling out like terms :

 7.1     Pull out like factors :

   7 - 21n  =   -7 • (3n - 1) 

Equation at the end of step  7  :

  1 - 3n  = 0 

Step  8  :

Solving a Single Variable Equation :

 8.1      Solve  :    -3n+1 = 0 

 Subtract  1  from both sides of the equation : 
                      -3n = -1
Multiply both sides of the equation by (-1) :  3n = 1


Divide both sides of the equation by 3:
                     n = 1/3 = 0.333

One solution was found :