To solve the equation \( 4(z - 5) + 2 = 4z - 18 \), we first simplify both sides.
Starting with the left side: \[ 4(z - 5) + 2 = 4z - 20 + 2 = 4z - 18 \]
Now, the equation becomes: \[ 4z - 18 = 4z - 18 \]
Now, we see that both sides of the equation are identical, which means that this equation is true for any value of \( z \).
Thus, the solution is that there are infinitely many solutions.
The correct response is: infinitely many.