To determine how many solutions the equation \(-3x + 3(5x + 2) = 2x + 10x + 9\) has, we will first simplify both sides of the equation step-by-step.
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Distribute on the left side: \[ -3x + 3(5x + 2) = -3x + 15x + 6 \] Combine like terms: \[ -3x + 15x + 6 = 12x + 6 \]
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Simplify the right side: \[ 2x + 10x + 9 = 12x + 9 \]
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Set the two sides equal to each other: \[ 12x + 6 = 12x + 9 \]
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Subtract \(12x\) from both sides: \[ 6 = 9 \]
This statement is false, which means there are no values of \(x\) that satisfy the equation. Therefore, the equation has no solutions.
Thus, the final answer is: No solutions.
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