Solve Fraction Equation 2F0514

1. **State the problem:** Solve the equation $$-\frac{2}{5} x = 10$$. 2. **Identify the goal:** We want to isolate $x$ on one side of the equation. 3. **Recall the rule:** To isolate $x$ when it is multiplied by a fraction, multiply both sides by the reciprocal of that fraction. 4. **Apply the reciprocal:** The reciprocal of $-\frac{2}{5}$ is $-\frac{5}{2}$. 5. **Multiply both sides by $-\frac{5}{2}$:** $$-\frac{5}{2} \times \left(-\frac{2}{5} x\right) = -\frac{5}{2} \times 10$$ 6. **Simplify the left side:** $$\cancel{-\frac{5}{2}} \times \cancel{-\frac{2}{5}} x = -\frac{5}{2} \times 10$$ Since $-\frac{5}{2} \times -\frac{2}{5} = 1$, this simplifies to: $$x = -\frac{5}{2} \times 10$$ 7. **Calculate the right side:** $$x = -\frac{5}{2} \times 10 = -\frac{5 \times 10}{2} = -\frac{50}{2} = -25$$ 8. **Final answer:** $$x = -25$$ **Therefore, the correct step to solve the equation is option b: Divide each side by $-\frac{2}{5}$.**