To solve the equation \( \frac{1}{6}x - 1 = 4 \), follow these steps:
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Add 1 to both sides to eliminate the -1 on the left side:
\[ \frac{1}{6}x - 1 + 1 = 4 + 1 \]
This simplifies to:
\[ \frac{1}{6}x = 5 \]
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Multiply both sides by 6 to solve for \( x \):
\[ 6 \cdot \frac{1}{6}x = 5 \cdot 6 \]
Simplifying this gives:
\[ x = 30 \]
So, the solution is \( x = 30 \).