Let's carefully analyze the steps Suzie took to solve the equation \(9x - 5 = 14(16x + 60)\).
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Start with the original equation: \[ 9x - 5 = 14(16x + 60) \]
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Distributing \(14\) on the right-hand side: Suzie wrote \(9x − 5 = 4x + 60\). However, we need to distribute \(14\) through \((16x + 60)\): \[ 14 \times 16x = 224x \quad \text{and} \quad 14 \times 60 = 840 \] Therefore: \[ 14(16x + 60) = 224x + 840 \] The correct equation is: \[ 9x - 5 = 224x + 840 \]
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Subsequent Steps: Suzie then tried to move \(4x\) from the right-hand side, but she used the wrong equation. Let's continue solving correctly from: \[ 9x - 5 = 224x + 840 \]
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Using subtraction property of equality to isolate \(x\): Subtract \(224x\) from both sides: \[ 9x - 224x - 5 = 840 \] This simplifies to: \[ -215x - 5 = 840 \]
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Using addition property of equality: Add \(5\) to both sides: \[ -215x = 845 \]
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Using division property of equality: Finally, divide by \(-215\): \[ x = \frac{845}{-215} \] This could be simplified depending on the numbers involved, but it will yield a different result than what Suzie found.
Conclusion: Suzie's mistake occurred in the first step, where she incorrectly distributed \(14\) through \((16x + 60)\). Instead of getting \(9x - 5 = 4x + 60\), the correct equation after distribution should have been \(9x - 5 = 224x + 840\). Therefore, all subsequent steps were based on incorrect information, leading to the wrong answer.
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