To determine if Suzie solved the equation correctly, let's analyze the steps she took and check for any errors.
The original equation is: \[ 9x - 5 = 14(16x + 60) \]
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Distributing on the right side: \[ 14(16x + 60) = 14 \cdot 16x + 14 \cdot 60 = 224x + 840 \] Thus, the equation becomes: \[ 9x - 5 = 224x + 840 \] Suzie's Step 1 was incorrect because she does not end up with \( 4x + 60 \).
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Continuing from the correct form: \[ 9x - 5 = 224x + 840 \]
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Using subtraction property of equality: 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: Divide both sides by -215: \[ x = -\frac{845}{215} = -\frac{169}{43} \]
Since Suzie's calculation did not follow the correct procedure from the start, she made a mistake in Step 1 where she incorrectly distributed \( \frac{1}{4} \).
Conclusion: The correct response is: Suzie made a mistake on Step 1 - she should have distributed the 14 to both \( 16x \) and \( 60 \) instead.
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