1. **Solve the inequality** $\frac{r}{2} + 15 > 45$. 2. Subtract 15 from both sides: $$\frac{r}{2} > 45 - 15$$ $$\frac{r}{2} > 30$$ 3. Multiply both sides by 2 to isolate $r$: $$r > 60$$ 4. **Interpretation:** The solution is all values of $r$ greater than 60, which matches the graph with an open circle at 60 and arrow to the right. --- 5. **Find the cost of 1 T-shirt given:** $$2x + 3y = 45$$ $$2x + 4y = 52$$ where $x$ is the cost of one jumper and $y$ is the cost of one T-shirt. 6. Subtract the first equation from the second: $$(2x + 4y) - (2x + 3y) = 52 - 45$$ $$2x - 2x + 4y - 3y = 7$$ $$y = 7$$ 7. **Answer:** The cost of one T-shirt is 7. --- 8. **Write down the inequality shown on the number line:** The number line shows a filled circle at 20 and arrow to the right. 9. This corresponds to: $$x \geq 20$$ --- 10. **Solve the inequality:** $$7 > a - 5$$ 11. Add 5 to both sides: $$7 + 5 > a$$ $$12 > a$$ 12. Rewrite as: $$a < 12$$ 13. The graph shows an open circle at 5 and arrow to the left, indicating $a < 5$, which is a stricter condition than $a < 12$. --- 14. **Solve the simultaneous equations:** $$3x + 7y = 54$$ $$3x + 3y = 6$$ 15. Subtract the second equation from the first: $$(3x + 7y) - (3x + 3y) = 54 - 6$$ $$3x - 3x + 7y - 3y = 48$$ $$4y = 48$$ $$y = 12$$ 16. Substitute $y=12$ into the second equation: $$3x + 3(12) = 6$$ $$3x + 36 = 6$$ $$3x = 6 - 36$$ $$3x = -30$$ $$x = -10$$ 17. **Solution:** $x = -10$, $y = 12$. --- **Final answers:** - Inequality solution: $r > 60$ - Cost of one T-shirt: 7 - Number line inequality: $x \geq 20$ - Inequality solution: $a < 12$ - Simultaneous equations solution: $x = -10$, $y = 12$