1. **Problem 1:** Anna has 500 and wants to buy notebooks costing 45 each. We need to find how many notebooks she can buy. 2. **Write the inequality:** Let $x$ be the number of notebooks. The total cost is $45x$ which must be less than or equal to 500 because she cannot spend more than she has. $$45x \leq 500$$ 3. **Solve the inequality:** Divide both sides by 45: $$x \leq \frac{500}{45}$$ Simplify the fraction: $$x \leq 11.11...$$ Since $x$ must be a whole number (you can't buy a fraction of a notebook), the maximum number of notebooks is 11. 4. **Answer:** Anna can buy up to 11 notebooks. 5. **Problem 2:** Solve and graph the inequality $x + 2 < 6$. 6. **Solve:** Subtract 2 from both sides: $$x < 6 - 2$$ $$x < 4$$ 7. **Problem 3:** Solve and graph the inequality $2x \geq 10$. 8. **Solve:** Divide both sides by 2: $$x \geq \frac{10}{2}$$ $$x \geq 5$$ 9. **Problem 4:** Solve and graph the inequality $-x + 3 > 1$. 10. **Solve:** Subtract 3 from both sides: $$-x > 1 - 3$$ $$-x > -2$$ Multiply both sides by -1 and reverse the inequality sign: $$x < 2$$ **Summary of solutions:** - $x \leq 11$ (number of notebooks) - $x < 4$ - $x \geq 5$ - $x < 2$ These inequalities can be graphed on a number line showing the solution regions accordingly.