1. **State the problem:** Solve the inequality $$2(x - 1) + 4x \leq 10$$. 2. **Expand and simplify:** Apply the distributive property to expand $$2(x - 1)$$: $$2x - 2 + 4x \leq 10$$ 3. **Combine like terms:** $$6x - 2 \leq 10$$ 4. **Isolate the variable term:** Add 2 to both sides: $$6x - 2 + 2 \leq 10 + 2$$ $$6x \leq 12$$ 5. **Divide both sides by 6:** $$\frac{\cancel{6}x}{\cancel{6}} \leq \frac{12}{6}$$ $$x \leq 2$$ 6. **Interpret the solution:** The solution to the inequality is all values of $$x$$ such that $$x \leq 2$$. **Final answer:** $$x \leq 2$$