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 :

                     7*b-2/5-(6*b-7/5)=0 

Step by step solution :

Step  1  :

            7
 Simplify   —
            5

Equation at the end of step  1  :

         2            7
  (7b -  —) -  (6b -  —)  = 0 
         5            5

Step  2  :

Rewriting the whole as an Equivalent Fraction :

 2.1   Subtracting a fraction from a whole

Rewrite the whole as a fraction using  5  as the denominator :

           6b     6b • 5
     6b =  ——  =  ——————
           1        5   

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:

 6b • 5 - (7)     30b - 7
 ————————————  =  ———————
      5              5   

Equation at the end of step  2  :

         2     (30b - 7)
  (7b -  —) -  —————————  = 0 
         5         5    

Step  3  :

            2
 Simplify   —
            5

Equation at the end of step  3  :

         2     (30b - 7)
  (7b -  —) -  —————————  = 0 
         5         5    

Step  4  :

Rewriting the whole as an Equivalent Fraction :

 4.1   Subtracting a fraction from a whole

Rewrite the whole as a fraction using  5  as the denominator :

           7b     7b • 5
     7b =  ——  =  ——————
           1        5   

Adding fractions that have a common denominator :

 4.2       Adding up the two equivalent fractions

 7b • 5 - (2)     35b - 2
 ————————————  =  ———————
      5              5   

Equation at the end of step  4  :

  (35b - 2)    (30b - 7)
  ————————— -  —————————  = 0 
      5            5    

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:

 (35b-2) - ((30b-7))     5b + 5
 ———————————————————  =  ——————
          5                5   

Step  6  :

Pulling out like terms :

 6.1     Pull out like factors :

   5b + 5  =   5 • (b + 1) 

Equation at the end of step  6  :

  b + 1  = 0 

Step  7  :

Solving a Single Variable Equation :

 7.1      Solve  :    b+1 = 0 

 Subtract  1  from both sides of the equation : 
                      b = -1

One solution was found :