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Solve for \( x \). \( \frac{4}{x-7}-\frac{6}{x-7}=2 \) If there is more than one solution, separate them with commas. If there is no solution, click on "No solution". \( x=\square \)

Ask by Harper Gonzalez. in the United States
Jan 05,2025

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\( x = 6 \)

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The Deep Dive

To solve the equation \( \frac{4}{x-7}-\frac{6}{x-7}=2 \), we can first combine the fractions on the left side. This gives us: \[ \frac{4 - 6}{x-7} = 2 \] Simplifying the numerator: \[ \frac{-2}{x-7} = 2 \] Next, we can cross-multiply to eliminate the fraction: \[ -2 = 2(x - 7) \] Now, distribute on the right side: \[ -2 = 2x - 14 \] To isolate \( x \), add 14 to both sides: \[ 12 = 2x \] Now, divide by 2: \[ x = 6 \] Now check for any restrictions: The fraction is undefined when \( x - 7 = 0 \) or \( x = 7 \). Since \( x = 6 \) does not cause any issues, we conclude: \( x = 6 \)

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