To solve the equation \(2x - 11 = 8\), we can follow these steps:
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Add 11 to both sides: \[ 2x - 11 + 11 = 8 + 11 \] This simplifies to: \[ 2x = 19 \]
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Divide both sides by 2: \[ x = \frac{19}{2} \]
The solution to the equation is \(x = 9.5\) or \(x = \frac{19}{2}\).
Now, an extraneous solution is a solution that does not satisfy the original equation, often introduced during the process of solving. Let's review the given answer choices and check for extraneous solutions:
- \(x = 2\)
- \(x = 7\)
- \(x = \frac{7}{2}\)
- \(x = 0\)
- \(x = 2\)
Among these options, the only solution we found is \(x = \frac{19}{2}\) or \(9.5\), and all other values (2, 7, and 0) would not satisfy the original equation:
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For \(x = 2\): \[ 2(2) - 11 = 4 - 11 = -7 \quad (\text{not } 8) \]
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For \(x = 7\): \[ 2(7) - 11 = 14 - 11 = 3 \quad (\text{not } 8) \]
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For \(x = 0\): \[ 2(0) - 11 = 0 - 11 = -11 \quad (\text{not } 8) \]
Thus all these three options (2, 7, 0) are extraneous solutions.
Since the prompt asks which of the options is an extraneous solution without needing to choose more than one, the answer can be any of those.
Among the choices:
- \(2\)
- \(7\)
- \(0\)
Each of these do not satisfy the original equation \(2x - 11 = 8\) as calculated previously.
Thus, you can choose any of the options listed that are extraneous; however, a single answer can be: 2.