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 :

                     -1/4*a-4-(7/4*a-3)=0 

Step by step solution :

Step  1  :

            7
 Simplify   —
            4

Equation at the end of step  1  :

       1          7
  ((0-(—•a))-4)-((—•a)-3)  = 0 
       4          4

Step  2  :

Rewriting the whole as an Equivalent Fraction :

 2.1   Subtracting a whole from a fraction

Rewrite the whole as a fraction using  4  as the denominator :

         3     3 • 4
    3 =  —  =  —————
         1       4  

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:

 7a - (3 • 4)     7a - 12
 ————————————  =  ———————
      4              4   

Equation at the end of step  2  :

          1                (7a - 12)
  ((0 -  (— • a)) -  4) -  —————————  = 0 
          4                    4    

Step  3  :

            1
 Simplify   —
            4

Equation at the end of step  3  :

          1                (7a - 12)
  ((0 -  (— • a)) -  4) -  —————————  = 0 
          4                    4    

Step  4  :

Rewriting the whole as an Equivalent Fraction :

 4.1   Subtracting a whole from a fraction

Rewrite the whole as a fraction using  4  as the denominator :

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

Adding fractions that have a common denominator :

 4.2       Adding up the two equivalent fractions

 -a - (4 • 4)     -a - 16
 ————————————  =  ———————
      4              4   

Equation at the end of step  4  :

  (-a - 16)    (7a - 12)
  ————————— -  —————————  = 0 
      4            4    

Step  5  :

Step  6  :

Pulling out like terms :

 6.1     Pull out like factors :

   -a - 16  =   -1 • (a + 16) 

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:

 (-a-16) - ((7a-12))     -8a - 4
 ———————————————————  =  ———————
          4                 4   

Step  7  :

Pulling out like terms :

 7.1     Pull out like factors :

   -8a - 4  =   -4 • (2a + 1) 

Equation at the end of step  7  :

  -2a - 1  = 0 

Step  8  :

Solving a Single Variable Equation :

 8.1      Solve  :    -2a-1 = 0 

 Add  1  to both sides of the equation : 
                      -2a = 1
Multiply both sides of the equation by (-1) :  2a = -1


Divide both sides of the equation by 2:
                     a = -1/2 = -0.500

One solution was found :