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Solve for \( w \). \[ \frac{2}{w}-\frac{1}{7}=\frac{5}{7 w} \] If there is more than one solution, separate them with commas. If there is no solution, click on "No solution". \( w=\square \)

Ask by Mathis Hanson. in the United States
Jan 05,2025

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\( w = 9 \)

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To solve the equation \[ \frac{2}{w} - \frac{1}{7} = \frac{5}{7w}, \] first, let's eliminate the fractions by multiplying both sides by \( 7w \) (assuming \( w \neq 0 \)): \[ 7w \left( \frac{2}{w} \right) - 7w \left( \frac{1}{7} \right) = 7w \left( \frac{5}{7w} \right). \] This simplifies to: \[ 14 - w = 5. \] Now, we can isolate \( w \): \[ 14 - 5 = w \implies w = 9. \] Therefore, the solution is: \( w = 9 \)

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