Solution - Linear equations with one unknown

Rearrange:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

                2/5+3/5*n-11/5-(2/5*n+1/5)=0 

Step by step solution :

Step  1  :

            1
 Simplify   —
            5

Equation at the end of step  1  :

    2  3     11    2    1
  ((—+(—•n))-——)-((—•n)+—)  = 0 
    5  5     5     5    5

Step  2  :

            2
 Simplify   —
            5

Equation at the end of step  2  :

    2  3     11    2    1
  ((—+(—•n))-——)-((—•n)+—)  = 0 
    5  5     5     5    5

Step  3  :

Adding fractions which have a common denominator :

 3.1       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:

 2n + 1     2n + 1
 ——————  =  ——————
   5          5   

Equation at the end of step  3  :

    2  3     11  (2n+1)
  ((—+(—•n))-——)-——————  = 0 
    5  5     5     5   

Step  4  :

            11
 Simplify   ——
            5 

Equation at the end of step  4  :

    2  3     11  (2n+1)
  ((—+(—•n))-——)-——————  = 0 
    5  5     5     5   

Step  5  :

            3
 Simplify   —
            5

Equation at the end of step  5  :

    2     3          11     (2n + 1)
  ((— +  (— • n)) -  ——) -  ————————  = 0 
    5     5          5         5    

Step  6  :

            2
 Simplify   —
            5

Equation at the end of step  6  :

    2    3n     11     (2n + 1)
  ((— +  ——) -  ——) -  ————————  = 0 
    5    5      5         5    

Step  7  :

Adding fractions which have a common denominator :

 7.1       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:

 2 + 3n     3n + 2
 ——————  =  ——————
   5          5   

Equation at the end of step  7  :

   (3n + 2)    11     (2n + 1)
  (———————— -  ——) -  ————————  = 0 
      5        5         5    

Step  8  :

Adding fractions which have a common denominator :

 8.1       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:

 (3n+2) - (11)     3n - 9
 —————————————  =  ——————
       5             5   

Equation at the end of step  8  :

  (3n - 9)    (2n + 1)
  ———————— -  ————————  = 0 
     5           5    

Step  9  :

Step  10  :

Pulling out like terms :

 10.1     Pull out like factors :

   3n - 9  =   3 • (n - 3) 

Adding fractions which have a common denominator :

 10.2       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:

 3 • (n-3) - ((2n+1))     n - 10
 ————————————————————  =  ——————
          5                 5   

Equation at the end of step  10  :

  n - 10
  ——————  = 0 
    5   

Step  11  :

When a fraction equals zero :

 11.1    When a fraction equals zero ...

Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.

Now,to get rid of the denominator, Tiger multiplys both sides of the equation by the denominator.

Here's how:

  n-10
  ———— • 5 = 0 • 5
   5  

Now, on the left hand side, the  5  cancels out the denominator, while, on the right hand side, zero times anything is still zero.

The equation now takes the shape :
   n-10  = 0

Solving a Single Variable Equation :

 11.2      Solve  :    n-10 = 0 

 Add  10  to both sides of the equation : 
                      n = 10

One solution was found :