Solution - Linear equations with one unknown

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "5.4" was replaced by "(54/10)".

Rearrange:

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

                     (54/10)/(2*y)-(9)=0 

Step by step solution :

Step  1  :

            27
 Simplify   ——
            5 

Equation at the end of step  1  :

  27         
  —— ÷ 2y -  9  = 0 
  5          

Step  2  :

         27      
 Divide  ——  by  2y
         5       

Equation at the end of step  2  :

   27    
  ——— -  9  = 0 
  10y    

Step  3  :

Rewriting the whole as an Equivalent Fraction :

 3.1   Subtracting a whole from a fraction

Rewrite the whole as a fraction using  10y  as the denominator :

         9     9 • 10y
    9 =  —  =  ———————
         1       10y  

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 :

 3.2       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:

 27 - (9 • 10y)     27 - 90y
 ——————————————  =  ————————
      10y             10y   

Step  4  :

Pulling out like terms :

 4.1     Pull out like factors :

   27 - 90y  =   -9 • (10y - 3) 

Equation at the end of step  4  :

  -9 • (10y - 3)
  ——————————————  = 0 
       10y      

Step  5  :

When a fraction equals zero :

 5.1    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:

  -9•(10y-3)
  —————————— • 10y = 0 • 10y
     10y    

Now, on the left hand side, the  10y  cancels out the denominator, while, on the right hand side, zero times anything is still zero.

The equation now takes the shape :
   -9  •  (10y-3)  = 0

Equations which are never true :

 5.2      Solve :    -9   =  0

This equation has no solution.
A a non-zero constant never equals zero.

Solving a Single Variable Equation :

 5.3      Solve  :    10y-3 = 0 

 Add  3  to both sides of the equation : 
                      10y = 3
Divide both sides of the equation by 10:
                     y = 3/10 = 0.300

One solution was found :