1. **State the problem:** Solve the equation $$3(x - 4) + 2 = 5x - 10$$ for $x$. 2. **Apply the distributive property:** Multiply 3 by each term inside the parentheses. $$3(x - 4) = 3 \times x - 3 \times 4 = 3x - 12$$ So the equation becomes: $$3x - 12 + 2 = 5x - 10$$ 3. **Combine like terms on the left side:** $$3x - 12 + 2 = 3x - 10$$ 4. **Rewrite the equation:** $$3x - 10 = 5x - 10$$ 5. **Isolate variable terms on one side:** Subtract $3x$ from both sides. $$\cancel{3x} - 10 - \cancel{3x} = 5x - 10 - 3x$$ which simplifies to: $$-10 = 2x - 10$$ 6. **Isolate constant terms on one side:** Add 10 to both sides. $$-10 + 10 = 2x - 10 + 10$$ which simplifies to: $$0 = 2x$$ 7. **Solve for $x$:** Divide both sides by 2. $$\frac{0}{\cancel{2}} = \frac{2x}{\cancel{2}}$$ which simplifies to: $$0 = x$$ **Final answer:** $$x = 0$$