Three times a number, add nine, divided by 6 is the same as the number itself. find the number

 The number is:  " 3 " .
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Explanation:
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Let "x" represent the "unknown number" ;  for which we are to solve. 
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         ; 

→  6x = 3x + 9 ; 
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Method 1)  
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Given:
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→  6x = 3x + 9 ; 

Subtract "3x" from each side of the equation; 

→  6x – 3x = 3x + 9 – 3x ; 

to get: 

→  3x = 9 ; 

Divide each side of the equation by " 3 " ;
   to isolate "x" on one side of the equation; & to solve for "x" ;

→  3x / 3 = 9 / 3 ;

→  x = 3 .
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The number is:  " 3 " .
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Method 2)
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Given:
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→  6x = 3x + 9 ; 

Divide the entire equation by " 3 " ;

     →  6x / 3 = (3x + 9) / 3 ;

to get:

     →      2x = x + 3 ; 

Subtract "x" from each side of the equation:

         →     2x – x  =  x + 3 – x  ; 

to get: 

              →   1x = 3 ; 

              ↔  " x = 3 " .
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The number is:  " 3 " .
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Main idea on left, details on right