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 $2x$ and $8x$: $$2x + 8x = 10x$$ So the equation simplifies to: $$10x - 10 = 20$$ 4. **Use the Addition Property of Equality:** Add 10 to both sides to isolate the term with $x$: $$10x - 10 + 10 = 20 + 10$$ This simplifies to: $$10x = 30$$ 5. **Use the Multiplication Property of Equality:** Multiply both sides by the multiplicative inverse of 10, which is $\frac{1}{10}$: $$\frac{1}{10} (10x) = \frac{1}{10} (30)$$ Show canceling common factors: $$\frac{\cancel{1}}{\cancel{10}} (\cancel{10}x) = \frac{1}{10} (30)$$ Simplifies to: $$x = 3$$ **Final answer:** $$x = 3$$