To solve the equation \(9x + 16 = 6x + 1\), we will first rearrange the equation to isolate \(x\).
- Start by subtracting \(6x\) from both sides:
\[ 9x - 6x + 16 = 1 \]
This simplifies to:
\[ 3x + 16 = 1 \]
- Next, subtract \(16\) from both sides:
\[ 3x + 16 - 16 = 1 - 16 \]
This simplifies to:
\[ 3x = -15 \]
- Now, divide both sides by \(3\) to solve for \(x\):
\[ x = \frac{-15}{3} \]
This simplifies to:
\[ x = -5 \]
Thus, the solution for \(x\) is
\[ \boxed{-5} \]
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