1. **State the problem:** Solve the equation $2x + 10 = 4x - 10$ for $x$. 2. **Write down the equation:** $$2x + 10 = 4x - 10$$ 3. **Isolate the variable terms on one side:** Subtract $2x$ from both sides: $$\cancel{2x} + 10 = 4x - 10 - \cancel{2x}$$ which simplifies to $$10 = 2x - 10$$ 4. **Isolate the constant terms on the other side:** Add $10$ to both sides: $$10 + 10 = 2x - 10 + 10$$ which simplifies to $$20 = 2x$$ 5. **Solve for $x$ by dividing both sides by 2:** $$\frac{20}{\cancel{2}} = \frac{2x}{\cancel{2}}$$ which simplifies to $$10 = x$$ 6. **Final answer:** $$x = 10$$