Let's go through Sehyr’s work step by step and identify the error.
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Starting with the equation: \[ w^2 - 7 = 11 \]
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She correctly added 7 to both sides: \[ w^2 - 7 + 7 = 11 + 7 \] This simplifies to: \[ w^2 = 18 \]
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However, Sehyr then incorrectly used the Division Property of Equality. She wrote: \[ w^2 = 18 \implies w^2/2 = 18/2 \] and ended up with: \[ w^2 = 9 \]
The last step "w²/2 = 18/2" was incorrect. Instead, we should take the square root of both sides of the equation \( w^2 = 18 \).
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Correcting from \( w^2 = 18 \): \[ w = \pm \sqrt{18} \] This can be simplified: \[ w = \pm \sqrt{9 \cdot 2} = \pm 3\sqrt{2} \]
Therefore, the correct solutions to the equation \( w^2 - 7 = 11 \) are: \[ w = 3\sqrt{2} \quad \text{and} \quad w = -3\sqrt{2} \]
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