Here are solutions to the given problems:

Simplify the following:

1. Problem 8: $3(2x - 4) - 2(1 - x)$ $6x - 12 - 2 + 2x = 8x - 14$

2. Problem 9: $-4(6 - 3x) - (x - 1)$ $-24 + 12x - x + 1 = 11x - 23$

3. Problem 10: $(4x - 8) \div 2$ $2x - 4$

4. Problem 11: $10.5 - 7\left(\frac{1}{3}x\right) + 10\left(\frac{1}{3}x\right)$ $10.5 - \frac{7x}{3} + \frac{10x}{3} = 10.5 + \frac{3x}{3} = 10.5 + x$

Multiply:

5. Problem 12: $\left(-\frac{2}{3}\right) \times \left(-\frac{5}{6}\right)$ $\frac{10}{18} = \frac{5}{9}$

6. Problem 13: $\left(\frac{4}{5}\right) \times \left(-\frac{9}{10}\right)$ $-\frac{36}{50} = -\frac{18}{25}$

7. Problem 14: $\left(-\frac{7}{8}\right) \times \left(\frac{6}{6}\right)$ $-\frac{7}{8}$

8. Problem 15: $\left(-\frac{4}{3}\right) \times \left(-\frac{5}{7}\right)$ $\frac{20}{21}$

Convert fraction to decimal:

9. Problem 16: $\frac{7}{9}$ $7 \div 9 = 0.\overline{7}$

10. Problem 17: $\frac{21}{16}$ $21 \div 16 = 1.3125$

Would you like further explanations or breakdowns for any specific problem?

Questions for Expansion:

1. Can you explain the distributive property used in Problems 8 and 9?
2. How do negative signs interact during multiplication of fractions, as seen in Problem 12?
3. How does division of fractions differ from multiplication, and could it apply to Problem 16?
4. Can you provide step-by-step methods for converting fractions to decimals?
5. How is simplifying expressions with variables different from simplifying constants?

Tip:

Always check your work step-by-step to catch minor sign or arithmetic errors that could lead to incorrect results.