1. **State the problem:** Solve the equation $2(x - 5) + 8x = 20$ for $x$. 2. **Apply the Distributive Property:** Multiply $2$ by each term inside the parentheses. $$2(x - 5) = 2x - 10$$ So the equation becomes: $$2x - 10 + 8x = 20$$ 3. **Combine like terms:** Add the $x$ terms together. $$2x + 8x = 10x$$ So the equation simplifies to: $$10x - 10 = 20$$ 4. **Isolate the variable term:** Add $10$ to both sides to cancel out $-10$. $$10x - 10 + \cancel{10} = 20 + \cancel{10}$$ $$10x = 30$$ 5. **Solve for $x$:** Divide both sides by $10$ to isolate $x$. $$\frac{1}{10}(10x) = \frac{1}{10}(30)$$ $$x = 3$$ **Final answer:** $x = 3$