1. **Problem (a):** Tom's car has lost 18% of its value and is now worth 18450. 2. **Formula:** If the original value is $V$, then after losing 18%, the value is $V - 0.18V = 0.82V$. 3. **Set up the equation:** $$0.82V = 18450$$ 4. **Solve for $V$:** $$V = \frac{18450}{0.82}$$ 5. **Intermediate step with cancellation:** $$V = \frac{\cancel{18450}}{\cancel{0.82}}$$ (just showing division) 6. **Calculate:** $$V = 22500$$ 7. **Answer for (a):** The car was originally worth 22500. --- 8. **Problem (b):** Solve the inequality $7 - 4x \geq 2x - 5$ where $x \in \mathbb{Z}$. 9. **Rearrange terms:** $$7 - 4x \geq 2x - 5$$ $$7 + 5 \geq 2x + 4x$$ $$12 \geq 6x$$ 10. **Divide both sides by 6:** $$\frac{12}{6} \geq \frac{6x}{6}$$ $$2 \geq x$$ 11. **Intermediate step with cancellation:** $$\frac{\cancel{12}}{\cancel{6}} \geq x$$ 12. **Solution:** $$x \leq 2$$ 13. **Since $x$ is an integer, the solution set is all integers less than or equal to 2.** --- **Final answers:** - (a) Original value of the car: 22500 - (b) Solution to inequality: $x \leq 2$, $x \in \mathbb{Z}$