Anumber is decreased by 3 and then the result is doubled. if the new result is 6 more than half the original number, what is the value of the original number?

The answer is:  " 8 " .

Explanation: 

Let "x" represent the "original number".

2(x - 3) = 6 + (1/2)x ;  Solve for "x" ;

Multiple the ENTIRE EQUATION (both sides) by "2" ; to get rid of the fraction:

2*{2(x - 3) = 6 + (1/2)x} ; 

to get:

4(x - 3) = 12 + x ; 

  Let us expand the "left-hand side" of the equation:

Note the "distributive property of multiplication" :

        a(b - c) = ab -  ac ; 
        
        a(b +c) = ab + ac ;

So;  "4(x - 3)" = 4*x - 4*3 = 4x - 12 ; 

Rewrite the equation:

  4x - 12 = 12 + x ;

Subtract "x" from EACH side of the equation; and Add "12" to EACH SIDE OF THE EQUATION; 

  4x - 12 - x + 12 = 12 + x - x + 12 ;

to get:

     3x = 24 ; 

Now, divide EACH side of the equation by "3" ; to isolate "x" on one side of the equation; and to solve for "x" ;

    3x/3 = 24/3 ; 

      x = 8 .