1. **State the problem:** Solve the inequality $$24 < 8x - 3 + x$$. 2. **Combine like terms:** On the right side, combine $$8x$$ and $$x$$ to get $$9x$$. $$24 < 9x - 3$$ 3. **Isolate the variable term:** Add 3 to both sides to move the constant term. $$24 + 3 < 9x - 3 + 3$$ $$27 < 9x$$ 4. **Divide both sides by 9:** To solve for $$x$$, divide both sides by 9. Since 9 is positive, the inequality direction stays the same. $$\frac{27}{\cancel{9}} < \frac{9x}{\cancel{9}}$$ $$3 < x$$ 5. **Rewrite the solution:** The solution to the inequality is $$x > 3$$. **Answer:** $$x > 3$$