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Papessa [141]
3 years ago
10

Two thirds of a number decreased by six is two. what is the number?

Mathematics
1 answer:
Kisachek [45]3 years ago
8 0
Answer:  The number is:  " 12 ". 

____________________________________
  Let "x" represent "the unknown number" (for which we wish to solve.

The expression:

\frac{2}{3} x  <span>− 6  =  2  ;   Solve for "x" ;  
</span>_______________________________________________
Method 1) 

   Add "6" to EACH SIDE of the equation;
_______________________________________________
       →   \frac{2}{3} x  − 6  + 6 =  2 + 6 ;

to get:

      →   \frac{2}{3} x = 8 ;
______________________________________________
Multiply each side of the equation by "\frac{3}{2}" ; to isolate "x" on one side of the equation ; and to solve for "x" ;
______________________________________________
     → \frac{3}{2} * \frac{2}{3} x = 8 * \frac{3}{2} ;

       →  x = 8 * \frac{3}{2} ;

                = \frac{8}{1} * \frac{3}{2} ;

                = \frac{8*3}{1*2} ;
       
                = \frac{24}{2} ;
 
                = <span>1<span>2 .</span></span>
______________________________________________
  x =  12 .
______________________________________________
Method 2)
______________________________________________
\frac{2}{3} x  − 6  =  2  ;   Solve for "x" ; 

   Add "6" to EACH SIDE of the equation;
_______________________________________________
       →   \frac{2}{3} x  − 6  + 6 =  2 + 6 ;

to get:
      →   \frac{2}{3} x = 8 ;
______________________________________________
Multiply each side of the equation by "3" ; to get rid of the "fraction" ;
               → 3 * \frac{2}{3} x = 8 * 3  ;
               → \frac{3}{1} * \frac{2}{3} x = 8 * 3 ;
               → \frac{3*2}{1*3}  x = 8 * 3 
               → \frac{6}{3} x = 24 ; 

                → 2x = 24 ;

 →  Divide each side of the equation by "2" ; to isolate "x" on one side of the equation; & to solve for "x" : 
 
                    2x / 2 = 24 / 2  ;

                        x = 12 .
__________________________________________________
Method 3).
__________________________________________________
\frac{2}{3} x  − 6  =  2  ;   Solve for "x" ;  
_______________________________________________
Add "6" to EACH SIDE of the equation;
_______________________________________________
       →   \frac{2}{3} x  − 6  + 6 =  2 + 6 ;

to get:

      →   \frac{2}{3} x = 8 ;
______________________________________________
Now, divide each side of the equation by " \frac{2}{3} " ;
  to isolate "x" on one side of the equation; & to solve for "x" ;
___________________________________________________
{\frac{2}{3} x }  /  {\frac{2}{3}}  =  8 / {\frac{2}{3}} ;

to get:  x =  8 / {\frac{2}{3}} ;

                =  8 * (\frac{3}{2} ;

                =  \frac{8}{1}  *  \frac{3}{2} ;

                =  \frac{8*3}{1*2} ;

                =  \frac{24}{2} ;

                = 12 ; 
___________________________________________
                         x = 12 .
___________________________________________
NOTE:  Variant:  (in "Methods 2 & 3") :
___________________________________________
At the point where:
___________________________________________
 =  8 * (\frac{3}{2}) ;

  =  \frac{8}{1}  *  \frac{3}{2} ;
__________________________________________
  We can cancel out the "2" to a "1" ; and we can cancel out the "8" to a "4" ;
__________________________________________
  {since: "8÷2 = 4" ; and since:  "2÷2 =1" } ;
__________________________________________
and we can rewrite the expression:
__________________________________________
 \frac{8}{1}  *  \frac{3}{2} ;
__________________________________________
as:   \frac{4}{1}  *  \frac{3}{1} ; 
__________________________________________
which equals:
__________________________________________
→  \frac{4*3}{1*1} ; 

   =   \frac{12}{1} ;

            =  12 .
__________________________________________
         x = 12 . 
__________________________________________
Answer:  The number is:  " 12 ". 
__________________________________________
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