1. **State the problem:** Solve the linear equation $$7u = -\frac{14}{3}$$ for $$u$$. 2. **Formula and rule:** To isolate $$u$$, use the multiplicative property of equality which states that you can divide both sides of the equation by the same nonzero number without changing the equality. 3. **Apply the property:** Divide both sides by 7: $$u = \frac{-\frac{14}{3}}{7}$$ 4. **Simplify the division:** Dividing by 7 is the same as multiplying by $$\frac{1}{7}$$: $$u = -\frac{14}{3} \times \frac{1}{7}$$ 5. **Multiply the fractions:** $$u = -\frac{14 \times 1}{3 \times 7} = -\frac{14}{21}$$ 6. **Simplify the fraction:** Both numerator and denominator are divisible by 7: $$u = -\frac{\cancel{14}^{2 \times 7}}{\cancel{21}^{3 \times 7}} = -\frac{2}{3}$$ 7. **Final answer:** $$u = -\frac{2}{3}$$