The image you uploaded again shows two limit problems. Here's a more detailed look at each:

1. Problem 19: $\lim_{{x \to 9}} (1 - \frac{1}{3}x) = -2$ This is a straightforward limit problem where the function is a linear expression. As $x$ approaches 9, plugging in 9 directly into the equation gives: $1 - \frac{1}{3} \times 9 = 1 - 3 = -2$ This confirms the given answer of -2.

2. Problem 20: $\lim_{{x \to 5}} (\frac{3}{2}x - \frac{1}{2}) = 7$ This is another direct substitution situation where the limit of the linear function as $x$ approaches 5 is: $\frac{3}{2} \times 5 - \frac{1}{2} = \frac{15}{2} - \frac{1}{2} = \frac{14}{2} = 7$ This result confirms the given answer of 7.

If you would like to understand any particular aspect of these limits or have further questions, please let me know! Here are some follow-up questions you might find helpful:

1. Would you like an explanation of why direct substitution works for these types of limit problems?
2. Are you interested in learning about situations where direct substitution might not be applicable for solving limits?
3. Would you like to explore the concept of one-sided limits?
4. How can understanding the behavior of linear functions help in other mathematical contexts?
5. Do you need help with more complex limit problems, perhaps involving rational or trigonometric functions?

Tip: Always check the function within the limit for any potential discontinuities or indeterminate forms before applying direct substitution. If such issues arise, alternative methods such as factoring, rationalization, or L'Hôpital's Rule may be necessary.