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 $V \times (1 - 0.18) = V \times 0.82$. 3. **Set up equation:** $$18450 = V \times 0.82$$ 4. **Solve for $V$:** $$V = \frac{18450}{0.82}$$ 5. **Intermediate step with cancellation:** $$V = \frac{18450}{\cancel{0.82}} \times \frac{\cancel{1}}{1}$$ 6. **Calculate:** $$V = 22500$$ 7. **Answer (a):** The car was originally worth 22500. --- 1. **Problem (b):** Solve the inequality $7 - 4x \geq 2x - 5$ where $x \in \mathbb{Z}$. 2. **Rearrange terms:** $$7 - 4x \geq 2x - 5$$ 3. **Bring all $x$ terms to one side and constants to the other:** $$7 + 5 \geq 2x + 4x$$ 4. **Simplify:** $$12 \geq 6x$$ 5. **Divide both sides by 6:** $$\frac{12}{6} \geq \frac{6x}{6}$$ 6. **Intermediate step with cancellation:** $$\frac{\cancel{12}}{\cancel{6}} \geq \cancel{\frac{6x}{6}}$$ 7. **Simplify:** $$2 \geq x$$ 8. **Rewrite inequality:** $$x \leq 2$$ 9. **Answer (b):** The solution set is all integers $x$ such that $x \leq 2$. --- 1. **Problem (c):** Solve the simultaneous equations: $$x^2 + y^2 = 41$$ $$2x - y = 3$$ 2. **Express $y$ from second equation:** $$y = 2x - 3$$ 3. **Substitute into first equation:** $$x^2 + (2x - 3)^2 = 41$$ 4. **Expand:** $$x^2 + (4x^2 - 12x + 9) = 41$$ 5. **Combine like terms:** $$5x^2 - 12x + 9 = 41$$ 6. **Bring all terms to one side:** $$5x^2 - 12x + 9 - 41 = 0$$ 7. **Simplify:** $$5x^2 - 12x - 32 = 0$$ 8. **Use quadratic formula:** $$x = \frac{12 \pm \sqrt{(-12)^2 - 4 \times 5 \times (-32)}}{2 \times 5}$$ 9. **Calculate discriminant:** $$144 + 640 = 784$$ 10. **Square root:** $$\sqrt{784} = 28$$ 11. **Calculate roots:** $$x = \frac{12 \pm 28}{10}$$ 12. **First root:** $$x = \frac{12 + 28}{10} = \frac{40}{10} = 4$$ 13. **Second root:** $$x = \frac{12 - 28}{10} = \frac{-16}{10} = -\frac{8}{5}$$ 14. **Since $x \in \mathbb{Z}$, discard $-\frac{8}{5}$ and keep $x=4$ only.** 15. **Find $y$ for $x=4$:** $$y = 2(4) - 3 = 8 - 3 = 5$$ 16. **Answer (c):** The integer solution is $(x,y) = (4,5)$.