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To solve the equation \(-20z + 9z + 5z + 9z - 20 = 4\), we first combine the like terms on the left side.
1. Combine the \(z\) terms:
\[
-20z + 9z + 5z + 9z = (-20 + 9 + 5 + 9)z = -20 + 23z = 23z - 20
\]
So, the equation simplifies to:
\[
23z - 20 = 4
\]
2. Next, we isolate \(z\) by adding 20 to both sides:
\[
23z = 4 + 20
\]
\[
23z = 24
\]
3. Now, divide both sides by 23 to solve for \(z\):
\[
z = \frac{24}{23}
\]
Thus, the solution to the equation is:
\[
z = \frac{24}{23}
\]