e the equation \( \frac{-7}{x}=\frac{7}{3 x}-10 \)

To solve the equation \( \frac{-7}{x}=\frac{7}{3 x}-10 \), first, we want to eliminate the fractions. We can do this by multiplying through by \( 3x \), which is the least common multiple of the denominators: \[ 3x \cdot \left(\frac{-7}{x}\right) = 3x \cdot \left(\frac{7}{3x}\right) - 3x \cdot 10 \] This simplifies to: \[ -21 = 7 - 30x \] Next, we can isolate \( x \) by adding \( 30x \) to both sides: \[ 30x - 21 = 7 \] Now, add \( 21 \) to both sides: \[ 30x = 28 \] Finally, divide both sides by \( 30 \): \[ x = \frac{28}{30} = \frac{14}{15} \] So, the solution is \( x = \frac{14}{15} \).