To find the equation that correctly leads to the final answer \( x = 8 \) using the given steps, we can work backwards from the final answer through the described operations: multiplying by -2 after subtracting 5.
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Starting with the final answer: \[ x = 8 \]
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The last step before \( x = 8 \) was multiplying by -2. Therefore, before this operation, the equation was: \[ -2 \cdot (x) = -16 \quad (\text{since } 8 \cdot -2 = -16) \] This implies: \[ x = \frac{-16}{-2} = 8 \]
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The expression before multiplying by -2 involved subtracting 5 from both sides, so: \[ \text{Before multiplying: } x - 5 = -16 \] Adding 5 to both sides gives: \[ x = -16 + 5 = -11 \]
Now we need to find an equation among the options provided that can eventually lead through these steps to the solution of \( x = 8 \).
Let's manipulate each option to check their validity:
A) \( \frac{x}{-2} + 5 = 1 \) \[ \frac{x}{-2} = 1 - 5 \implies \frac{x}{-2} = -4 \implies x = 8 \text{ (Correct after these steps)} \]
B) \( \frac{x}{2} + 5 = 1 \) \[ \frac{x}{2} = 1 - 5 \implies \frac{x}{2} = -4 \implies x = -8 \text{ (Incorrect)} \]
C) \( \frac{x}{-2} - 5 = 1 \) \[ \frac{x}{-2} = 1 + 5 \implies \frac{x}{-2} = 6 \implies x = -12 \text{ (Incorrect)} \]
D) \( \frac{x}{2} - 5 = 1 \) \[ \frac{x}{2} = 1 + 5 \implies \frac{x}{2} = 6 \implies x = 12 \text{ (Incorrect)} \]
From the above checks, we can see that option A leads to \( x = 8 \) correctly, affirming the processes described in the question.
Thus, the correct answer is: A) \(\frac{x}{-2} + 5 = 1\).
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