1. **State the problem:** Solve the inequality $$5x + 2 \leq 3x + 10$$. 2. **Write down the inequality:** $$5x + 2 \leq 3x + 10$$. 3. **Subtract $3x$ from both sides:** $$5x + 2 - 3x \leq 3x + 10 - 3x$$ $$\Rightarrow 2x + 2 \leq 10$$ 4. **Subtract 2 from both sides:** $$2x + 2 - 2 \leq 10 - 2$$ $$\Rightarrow 2x \leq 8$$ 5. **Divide both sides by 2:** $$\frac{\cancel{2}x}{\cancel{2}} \leq \frac{8}{2}$$ $$\Rightarrow x \leq 4$$ 6. **Final answer:** $$x \leq 4$$ This means the solution to the inequality is all values of $x$ less than or equal to 4.