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 :

                     3-1/2*d-(3/2*d+4-d)=0 

Step by step solution :

Step  1  :

            3
 Simplify   —
            2

Equation at the end of step  1  :

      1        3
  (3-(—•d))-(((—•d)+4)-d)  = 0 
      2        2

Step  2  :

Rewriting the whole as an Equivalent Fraction :

 2.1   Adding a whole to a fraction

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:

 3d + 4 • 2     3d + 8
 ——————————  =  ——————
     2            2   

Equation at the end of step  2  :

         1           (3d + 8)    
  (3 -  (— • d)) -  (———————— -  d)  = 0 
         2              2        

Step  3  :

Rewriting the whole as an Equivalent Fraction :

 3.1   Subtracting a whole from a fraction

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

         d     d • 2
    d =  —  =  —————
         1       2  

Adding fractions that have a common denominator :

 3.2       Adding up the two equivalent fractions

 (3d+8) - (d • 2)     d + 8
 ————————————————  =  —————
        2               2  

Equation at the end of step  3  :

         1          (d + 8)
  (3 -  (— • d)) -  ———————  = 0 
         2             2   

Step  4  :

            1
 Simplify   —
            2

Equation at the end of step  4  :

         1          (d + 8)
  (3 -  (— • d)) -  ———————  = 0 
         2             2   

Step  5  :

Rewriting the whole as an Equivalent Fraction :

 5.1   Subtracting a fraction from a whole

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

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

Adding fractions that have a common denominator :

 5.2       Adding up the two equivalent fractions

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

Equation at the end of step  5  :

  (6 - d)    (d + 8)
  ——————— -  ———————  = 0 
     2          2   

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:

 (6-d) - ((d+8))     -2d - 2
 ———————————————  =  ———————
        2               2   

Step  7  :

Pulling out like terms :

 7.1     Pull out like factors :

   -2d - 2  =   -2 • (d + 1) 

Equation at the end of step  7  :

  -d - 1  = 0 

Step  8  :

Solving a Single Variable Equation :

 8.1      Solve  :    -d-1 = 0 

 Add  1  to both sides of the equation : 
                      -d = 1
Multiply both sides of the equation by (-1) :  d = -1

One solution was found :