Step 1 :The given equation is \(9 + z = -14\).
Step 2 :To solve for \(z\), we need to isolate \(z\) on one side of the equation. We can do this by subtracting 9 from both sides of the equation.
Step 3 :This gives us \(z = -14 - 9\).
Step 4 :Solving this, we find that \(z = -23\).
Step 5 :We can check this solution by substitifying \(z = -23\) into the original equation and verifying that both sides of the equation are equal.
Step 6 :Substituting \(z = -23\) into the original equation gives us \(9 + (-23) = -14\).
Step 7 :Solving this, we find that the left side of the equation equals the right side, confirming that \(z = -23\) is the correct solution.
Step 8 :Final Answer: The solution to the equation is \(\boxed{-23}\).