The standard mantra to solve is as follows:


    subtract '30' from both sides.  You will get

        45x = 120-30,

        45x = 90.


     Now divide both sides by 45.  You will get

         x =  = 2.


     ANSWER.  The solution to given equation is  x = 2.


     CHECK.  We substitute x= 2 into the left side of the given equation.  It gives the value 

                       45*2 + 30 = 90 + 30 = 120,

                    the same as the right side of the given equation.

                    This check CONFIRMS that the solution x = 2  is  CORRECT.

Solve: 45x + 30 = 120
x = 12
x = 10
x = 6
x = 2

I think that this student may have only gotten to the stage of finding
solutions by trial and error by substitution.

      Try x = 12
   45x + 30 = 120
45(12) + 30 = 120
   540 + 30 = 120
        570 = 120, so x = 12 is NOT the correct answer.

      Try x = 10
   45x + 30 = 120
45(10) + 30 = 120
   450 + 30 = 120
        480 = 120, so x = 10 is NOT the correct answer.

      Try x = 6
   45x + 30 = 120
 45(6) + 30 = 120
   270 + 30 = 120
        300 = 120, so x = 6 is NOT the correct answer.

      Try x = 2
   45x + 30 = 120
 45(2) + 30 = 120
    90 + 30 = 120
        120 = 120, so x = 2 IS the correct answer.

Edwin