*will give brainliest* what is the value of x? enter your answer in the box. x =

The answer is:  " x = 54 " .

Explanation:


Note:  The two expressions shown are "equal" to each other;  since they are "vertical angles" ;  and vertical angles are equal.

So,  2x + 2 = 3x - 52 ;   solve for "x" ; 

Subtract "2x" from each side of the equation ; & subtract "2" from each side of the equation; & add "52" to each side of the equation:

      2x + 2 - 2x - 2 + 52 = 3x - 52 - 2x - 2 + 52 ; 

to get : 

      52 = x - 2 ; 

Add "2" to each side of the equation; 
      to isolate "x" on one side of the equation; & to solve for "x" ; 

     52 + 2 = x - 2 + 2 ; 

to get:  

    54 = x ;  ↔  " x = 54 "; 

The answer is:  " x = 54 " .

Now, let us check our answer;  by plugging in "54" for "x" ; into our original equation;  to see if the equation holds true;  that is; to see if both sides of the equation are equal when "x = 54" ; 

  →   2x + 2  =  3x - 52 ; 

  →  2(54) + 2 = ? 3(54) - 52 ?? ; 

  →  108 + 2  = ?  162 - 56 ?? ; 

  →  110 = ?  110 ?? ;  →  Yes!