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 :

                     1/216-(6^2*x-1)=0 

Step by step solution :

Step  1  :

 1.1     6 = 2•3

(6)² = (2•3)² = 2² • 3²

Equation at the end of step  1  :

   1                         
  ——— -  (((22•32) • x) -  1)  = 0 
  216                        

Step  2  :

             1 
 Simplify   ———
            216

Equation at the end of step  2  :

   1     
  ——— -  (36x - 1)  = 0 
  216    

Step  3  :

Rewriting the whole as an Equivalent Fraction :

 3.1   Subtracting a whole from a fraction

Rewrite the whole as a fraction using  216  as the denominator :

               36x - 1     (36x - 1) • 216
    36x - 1 =  ———————  =  ———————————————
                  1              216      

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:

 1 - ((36x-1) • 216)     217 - 7776x
 ———————————————————  =  ———————————
         216                 216    

Equation at the end of step  3  :

  217 - 7776x
  ———————————  = 0 
      216    

Step  4  :

When a fraction equals zero :

 4.1    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:

  217-7776x
  ————————— • 216 = 0 • 216
     216   

Now, on the left hand side, the  216  cancels out the denominator, while, on the right hand side, zero times anything is still zero.

The equation now takes the shape :
   217-7776x  = 0

Solving a Single Variable Equation :

 4.2      Solve  :    -7776x+217 = 0 

 Subtract  217  from both sides of the equation : 
                      -7776x = -217
Multiply both sides of the equation by (-1) :  7776x = 217


Divide both sides of the equation by 7776:
                     x = 217/7776 = 0.028

One solution was found :