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 :

                     1/2*r-3-((4-3/2*r))=0 

Step by step solution :

Step  1  :

            3
 Simplify   —
            2

Equation at the end of step  1  :

    1           3
  ((—•r)-3)-(4-(—•r))  = 0 
    2           2

Step  2  :

Rewriting the whole as an Equivalent Fraction :

 2.1   Subtracting a fraction from a whole

Rewrite the whole as a fraction using  2  as the denominator :

          4     4 • 2
     4 =  —  =  —————
          1       2  

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:

 4 • 2 - (3r)     8 - 3r
 ————————————  =  ——————
      2             2   

Equation at the end of step  2  :

    1               (8 - 3r)
  ((— • r) -  3) -  ————————  = 0 
    2                  2    

Step  3  :

            1
 Simplify   —
            2

Equation at the end of step  3  :

    1               (8 - 3r)
  ((— • r) -  3) -  ————————  = 0 
    2                  2    

Step  4  :

Rewriting the whole as an Equivalent Fraction :

 4.1   Subtracting a whole from a fraction

Rewrite the whole as a fraction using  2  as the denominator :

         3     3 • 2
    3 =  —  =  —————
         1       2  

Adding fractions that have a common denominator :

 4.2       Adding up the two equivalent fractions

 r - (3 • 2)     r - 6
 ———————————  =  —————
      2            2  

Equation at the end of step  4  :

  (r - 6)    (8 - 3r)
  ——————— -  ————————  = 0 
     2          2    

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:

 (r-6) - ((8-3r))     4r - 14
 ————————————————  =  ———————
        2                2   

Step  6  :

Pulling out like terms :

 6.1     Pull out like factors :

   4r - 14  =   2 • (2r - 7) 

Equation at the end of step  6  :

  2r - 7  = 0 

Step  7  :

Solving a Single Variable Equation :

 7.1      Solve  :    2r-7 = 0 

 Add  7  to both sides of the equation : 
                      2r = 7
Divide both sides of the equation by 2:
                     r = 7/2 = 3.500

One solution was found :