1. **State the problem:** Solve the equation $$\frac{2}{7} (z - 10) = -3$$ for $z$. 2. **Use the distributive property and isolate $z$:** Multiply both sides by 7 to eliminate the denominator. $$7 \times \frac{2}{7} (z - 10) = 7 \times (-3)$$ 3. **Simplify the left side by canceling 7:** $$\cancel{7} \times \frac{2}{\cancel{7}} (z - 10) = -21$$ which simplifies to $$2 (z - 10) = -21$$ 4. **Divide both sides by 2 to isolate $(z - 10)$:** $$\frac{2 (z - 10)}{2} = \frac{-21}{2}$$ 5. **Simplify by canceling 2:** $$\cancel{2} (z - 10) / \cancel{2} = -\frac{21}{2}$$ which gives $$z - 10 = -\frac{21}{2}$$ 6. **Add 10 to both sides to solve for $z$:** $$z = 10 - \frac{21}{2}$$ 7. **Convert 10 to a fraction with denominator 2:** $$z = \frac{20}{2} - \frac{21}{2} = \frac{20 - 21}{2} = -\frac{1}{2}$$ **Final answer:** $$z = -\frac{1}{2}$$