1. **Stating the problem:** Solve the inequality $$3x + 5 - 4x < 8x + 3 + 2x$$. 2. **Formula and rules:** To solve linear inequalities, we first simplify both sides, then isolate the variable on one side. Remember, when dividing or multiplying by a negative number, the inequality sign reverses. 3. **Simplify both sides:** $$3x + 5 - 4x = (3x - 4x) + 5 = -x + 5$$ $$8x + 3 + 2x = (8x + 2x) + 3 = 10x + 3$$ 4. **Rewrite the inequality:** $$-x + 5 < 10x + 3$$ 5. **Bring all terms involving $x$ to one side and constants to the other:** $$-x - 10x < 3 - 5$$ $$-11x < -2$$ 6. **Divide both sides by $-11$ and reverse the inequality sign because dividing by a negative:** $$x > \cancel{-11x}/\cancel{-11} > \cancel{-2}/\cancel{-11}$$ $$x > \frac{2}{11}$$ 7. **Final answer:** $$\boxed{x > \frac{2}{11}}$$