Let's look at Sehyr's work step by step to identify the error and find the correct solution.
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The original equation is: \[ w^2 - 7 = 11 \]
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Sehyr correctly applied the Addition Property of Equality to isolate \(w^2\): \[ w^2 - 7 + 7 = 11 + 7 \rightarrow w^2 = 18 \] Here, she correctly added 7 to both sides of the equation.
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However, the subsequent step is where she made an error: \[ w^2 = 18 \] From this point, she incorrectly stated \(w^2\) as \(w^2/2 = 18/2\) and went on to solve for \(w\) as: \[ w = 9 \]
This is incorrect.
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The correct next step after \(w^2 = 18\) is to take the square root of both sides: \[ w = \sqrt{18} \] Since square roots can be both positive and negative, we also have: \[ w = \pm \sqrt{18} \]
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Simplifying \(\sqrt{18}\): \[ \sqrt{18} = \sqrt{9 \cdot 2} = \sqrt{9} \cdot \sqrt{2} = 3\sqrt{2} \]
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Therefore, the complete solution is: \[ w = 3\sqrt{2} \quad \text{or} \quad w = -3\sqrt{2} \]
In conclusion, the error in Sehyr's work was in the incorrect simplification after isolating \(w^2\). The correct solutions are: \[ w = 3\sqrt{2} \quad \text{and} \quad w = -3\sqrt{2} \]