Determine the solution to f(x) = g(x) using the following system of equations:

f(x) = 3x − 23
g(x) = −4.5x + 7

In this item, we equate the functions as stated.
             f(x) = g(x)
          3x - 23 = -4.5x + 7

Transpose all the terms with variables to one side of the equation and all the constants to the other side. This is shown below.
         3x + 4.5x = 7 + 23

Combine like terms,
             7.5x = 30
Divide both sides of the equation by 7.5.
            (7.5x)/7.5 = 30/(7.5)
                   x = 4

Therefore, the solution to this item is that x = 4.