1. **State the problem:** Solve the equation $$10.5 = 4x - 4.5 - 3x$$ for $x$. 2. **Rewrite the equation:** Combine like terms on the right side. $$4x - 3x - 4.5 = 10.5$$ 3. **Simplify:** $$x - 4.5 = 10.5$$ 4. **Isolate $x$:** Add $4.5$ to both sides. $$x = 10.5 + 4.5$$ 5. **Calculate:** $$x = 15$$ **Final answer:** $x = 15$