Your solution process is mostly correct, but there’s a minor mistake in the notation during the division step. Let’s clarify each step to ensure accuracy:
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Isolate the term with y: Subtract \( x \) from both sides of the equation: \[ 3xy + x - x = 33 - x \implies 3xy = 33 - x \]
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Solve for y: Divide both sides by \( 3x \) (assuming \( x \neq 0 \)): \[ y = \frac{33 - x}{3x} \]
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Simplify the expression: You can split the fraction: \[ y = \frac{33}{3x} - \frac{x}{3x} = \frac{11}{x} - \frac{1}{3} \]
Thus, the correct expression for \( y \) is: \[ y = \frac{11}{x} - \frac{1}{3} \]
If \( x = 3 \), we can see that \( y = 11 - x/3 \) becomes \( 11 - 1 = 10 \). However, the simplified final expression \( y = \frac{11}{x} - \frac{1}{3} \) varies based on the value of \( x \).
So, please ensure the division and simplification steps are properly interpreted based on the dependencies of \( y \) on \( x \).