1. Let's start with a simple algebra exercise: Solve for $x$ in the equation $$2x + 3 = 11$$. 2. Use the formula for linear equations: $$ax + b = c \implies x = \frac{c - b}{a}$$. 3. Substitute the values: $$x = \frac{11 - 3}{2}$$. 4. Simplify the numerator: $$x = \frac{8}{2}$$. 5. Divide to find the solution: $$x = 4$$. 6. Next, try a quadratic equation: Solve $$x^2 - 5x + 6 = 0$$. 7. Use the factoring method: Find two numbers that multiply to 6 and add to -5, which are -2 and -3. 8. Factor the quadratic: $$(x - 2)(x - 3) = 0$$. 9. Set each factor equal to zero: $$x - 2 = 0$$ or $$x - 3 = 0$$. 10. Solve each: $$x = 2$$ or $$x = 3$$. 11. Finally, try a physics problem involving motion: Calculate the distance traveled if an object moves at a speed of 10 m/s for 5 seconds. 12. Use the formula: $$\text{distance} = \text{speed} \times \text{time}$$. 13. Substitute the values: $$\text{distance} = 10 \times 5$$. 14. Calculate the distance: $$\text{distance} = 50$$ meters. These exercises cover algebraic equations and basic physics calculations to practice problem-solving skills.