To find the equation that leads to the final answer of \(x = 8\) after following the given directions, we can reverse-engineer the steps.
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Start with the final answer: \(x = 8\).
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The last operation performed was multiplying both sides by \(-2\). To find the value before this operation, we need to divide by \(-2\):
\[ 8 \div -2 = -4 \]
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Before we multiplied by \(-2\), we must have subtracted \(5\) from both sides. So, we need to add \(5\) to \(-4\):
\[ -4 + 5 = 1 \]
Now, we know that before we performed the operations, we had the equation:
\[ x - 5 = 1 \]
Next, let's see if any of the given options yield this result when we apply the operations.
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For \(x^2 + 5 = 1\): \[ x^2 + 5 - 5 = 1 - 5 \Rightarrow x^2 = -4 \quad (\text{not applicable}) \]
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For \(x - 2 + 5 = 1\): \[ x - 2 + 5 - 5 = 1 - 5 \Rightarrow x - 2 = -4 \Rightarrow x = -2 + 4 = 2 \quad (\text{not applicable}) \]
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For \(x^2 - 5 = 1\): \[ x^2 - 5 + 5 = 1 + 5 \Rightarrow x^2 = 6 \quad (\text{not applicable}) \]
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For \(x - 2 - 5 = 1\): \[ x - 2 - 5 + 5 = 1 + 5 \Rightarrow x - 2 = 6 \Rightarrow x = 6 + 2 = 8 \quad (\text{this matches}) \]
Only the last option leads to the correct answer, so the correct equation is:
\[ x - 2 - 5 = 1 \]