To solve the equation \( 9(x + 1) = 3(5x + 1) - 12 \), we will start by simplifying both sides step by step.
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Expand both sides: \[ 9(x + 1) = 9x + 9 \] \[ 3(5x + 1) - 12 = 15x + 3 - 12 = 15x - 9 \]
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Now we can rewrite the equation: \[ 9x + 9 = 15x - 9 \]
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Next, let's get all terms involving \( x \) on one side and constant terms on the other side: \[ 9 + 9 = 15x - 9x \] \[ 18 = 6x \]
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Solve for \( x \): \[ x = \frac{18}{6} = 3 \]
We found that \( x = 3 \).
Next, we check if there are any other solutions by examining the original equation. Since it resulted in a single equation with one solution (linear equation), we conclude that:
The equation has one solution: \( x = 3 \).
Thus, the correct response is: The equation has one solution: x equals 3.