Solve for x: 1 over 3 (2x − 8) = 4. a. 2 b. 6 c. 10 d. 10 over 3 !

The correct answer is:  [C]:  "10" . 

    →  " x = 10 "  .

Explanation:

 Given:

    →   (1/3) * (2x − 8) = 4  ;  Solve for "x" ; 

To get rid of the "fraction" ; multiple BOTH SIDE of the equation by "3" : 

   →   3 * { (1/3) * (2x − 8) } = 3 * 4 ; 

to get: 

 1(2x − 8) = 12 ; 

↔  2x − 8 = 12 ; 

Add "8" to BOTH SIDES of the equation ; 

 →  2x − 8 + 8 = 12 + 8 ;

to get:

→  2x = 20 ; 

Divide EACH SIDE of the equation by "2" ; 
 to isolate "x" on one side of the equation; & to solve for "x" 

→ 2x / 2  = 20/ 2 ; 

→  x = 10  ;  which is:  Answer choice:  [C]:  "10" .

Let us check our  " x = 10" ;  by plugging in "10" for all values of "x" into the original equation; to see if the answer holds true for the equation ; that is, to see if both sides of the equation are equal when "x = 10" ; 

The original equation:  " (1/3) * (2x − 8) = 4 " .

    →  (1/3) * [2(10) − 8)  =?  4 ?? ;

    →  (1/3) * [20 − 8)  =?  4 ?? ; 

    →  (1/3) * (12)  =?  4 ?? ;   Yes!