Solve for \( u \) \[ 6 u=-\frac{12}{7} \]

To solve for \( u \) in the equation: \[ 6 u = -\frac{12}{7} \] follow these steps: 1. **Isolate \( u \):** To solve for \( u \), divide both sides of the equation by 6. \[ u = \frac{-\frac{12}{7}}{6} \] 2. **Simplify the Right Side:** Dividing by 6 is the same as multiplying by \( \frac{1}{6} \). \[ u = -\frac{12}{7} \times \frac{1}{6} \] 3. **Multiply the Fractions:** Multiply the numerators together and the denominators together. \[ u = \frac{-12 \times 1}{7 \times 6} = \frac{-12}{42} \] 4. **Reduce the Fraction:** Simplify \( \frac{-12}{42} \) by dividing both the numerator and the denominator by their greatest common divisor, which is 6. \[ u = \frac{-12 \div 6}{42 \div 6} = \frac{-2}{7} \] **Final Answer:** \[ u = -\frac{2}{7} \]