If the product of 4 and a number is decreased by 12, the result is twice the opposite of the number. find the number. explain ♥

 The number is:  "2 " .

Explanation:

Write the expression; which is an equation, as follows:

     " 4x − 12 = 2(-x) " ;  in which "x" represents "the number for which we shall                                       solve" .

Note:  

If the "number" = "x" ;  the "opposite of the number"  =  " -x " ;

Rewrite as:  " 4x − 12 = -2x " ;

     →  Add "12" ; & add "2x" ; to EACH SIDE of the equation:

                      4x − 12 + 12 + 2x = -2x + 12 + 2x ;

           to get:    6x  = 12  ;

 Now, divide each side of the equation by "6" ; 
     to isolate "x" on one side of the equation; & to solve for "x" ;

                         6x / 6  =  12 / 6 ;

                    to get:    x = 2 .

 The number is:  "2 " .

Let us check our answer, by plugging in "2" for "x" in our original equation:

        →   " 4x − 12 = 2(-x) " ;

  Let us plug in "2" for "x" ; to see if the equation holds true; that is; if both side of the equation are equal; when "x = 2" ;

        →   " 4(2) − 12 = ?  2(-2) ?? 

        →    8 − 12 = ?  -4 ? ;
 
        →    -4 = ? -4 ??  Yes!
     

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