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 :

                1/3*(z+4)-6-(2/3*(5-z))=0 

Step by step solution :

Step  1  :

            2
 Simplify   —
            3

Equation at the end of step  1  :

    1            2
  ((—•(z+4))-6)-(—•(5-z))  = 0 
    3            3

Step  2  :

Equation at the end of step  2  :

    1           2•(5-z)
  ((—•(z+4))-6)-———————  = 0 
    3              3   

Step  3  :

            1
 Simplify   —
            3

Equation at the end of step  3  :

    1                     2 • (5 - z)
  ((— • (z + 4)) -  6) -  ———————————  = 0 
    3                          3     

Step  4  :

Equation at the end of step  4  :

   (z + 4)          2 • (5 - z)
  (——————— -  6) -  ———————————  = 0 
      3                  3     

Step  5  :

Rewriting the whole as an Equivalent Fraction :

 5.1   Subtracting a whole from a fraction

Rewrite the whole as a fraction using  3  as the denominator :

         6     6 • 3
    6 =  —  =  —————
         1       3  

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 :

 5.2       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:

 (z+4) - (6 • 3)     z - 14
 ———————————————  =  ——————
        3              3   

Equation at the end of step  5  :

  (z - 14)    2 • (5 - z)
  ———————— -  ———————————  = 0 
     3             3     

Step  6  :

Adding fractions which have a common denominator :

 6.1       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:

 (z-14) - (2 • (5-z))     3z - 24
 ————————————————————  =  ———————
          3                  3   

Step  7  :

Pulling out like terms :

 7.1     Pull out like factors :

   3z - 24  =   3 • (z - 8) 

Equation at the end of step  7  :

  z - 8  = 0 

Step  8  :

Solving a Single Variable Equation :

 8.1      Solve  :    z-8 = 0 

 Add  8  to both sides of the equation : 
                      z = 8

One solution was found :