To solve the equation \( 3(22 - 4) = 7 - (z + 5) \), we will follow these steps:
First, simplify the left side:
\[ 3(22 - 4) = 3 \times 18 = 54 \]
Now, simplify the right side:
\[ 7 - (z + 5) = 7 - z - 5 = 2 - z \]
Now we have the equation:
\[ 54 = 2 - z \]
Next, isolate \( z \). First, subtract 2 from both sides:
\[ 54 - 2 = -z \]
This simplifies to:
\[ 52 = -z \]
Now, multiply both sides by -1 to solve for \( z \):
\[ z = -52 \]
Thus, the solution is:
\[ z = -52 \]