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