Let's go through Sehyr's work step by step to identify the error:
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Original Equation: \[ w^2 - 7 = 11 \]
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Add 7 to Both Sides: Sehyr correctly added 7 to both sides: \[ w^2 - 7 + 7 = 11 + 7 \] This simplifies to: \[ w^2 = 18 \]
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Error in the Next Step: The mistake occurs in the next step. Sehyr wrote: \[ w^2 = 18 \] However, instead of dividing the equation simply as \( w^2 = 18 \), she mistakenly wrote: \[ w^2 = 182 \] This is incorrect.
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Taking the Square Root: The correct step is to take the square root of both sides of \( w^2 = 18 \): \[ w = \pm \sqrt{18} \] Which can be simplified: \[ w = \pm \sqrt{9 \cdot 2} = \pm 3\sqrt{2} \]
Thus, the 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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