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To solve the equation \( 4z + 1 = 41 \), follow these steps:
1. Subtract \( 1 \) from both sides:
\[
4z + 1 - 1 = 41 - 1
\]
\[
4z = 40
\]
2. Divide both sides by \( 4 \):
\[
z = \frac{40}{4}
\]
\[
z = 10
\]
So, the solution is \( z = 10 \).