Let’s simplify each expression by combining like terms step by step:

1. $5n + 11n$
Combine the like terms ($n$-terms):
$5n + 11n = 16n$
Answer: $16n$

2. $-6k + 7k$
Combine the like terms ($k$-terms):
-6k + 7k = 1k \quad \text{(or simply k)}.
Answer: $k$

3. $-8x - 12x$
Combine the like terms ($x$-terms):
$-8x - 12x = -20x$
Answer: $-20x$

4. $-v + 12v$
Combine the like terms ($v$-terms):
$-v + 12v = 11v$
Answer: $11v$

5. $a + 4 - 9 + 5a$
Combine the like terms:

• Combine the $a$-terms:
  $a + 5a = 6a$
• Combine the constants:
  $4 - 9 = -5$
  Final expression:
  $6a - 5$
  Answer: $6a - 5$

6. $12r + 5 + 3r - 5$
Combine the like terms:

• Combine the $r$-terms:
  $12r + 3r = 15r$
• Combine the constants:
  $5 - 5 = 0$
  Final expression:
  $15r$
  Answer: $15r$

7. $-5 + 9n + 6$
Combine the like terms:

• Combine the constants:
  $-5 + 6 = 1$
  Final expression:
  $9n + 1$
  Answer: $9n + 1$

8. $4x + 5y - 9x - 2y + 7xy$
Combine the like terms:

• Combine the $x$-terms:
  $4x - 9x = -5x$
• Combine the $y$-terms:
  $5y - 2y = 3y$
• The $xy$-term is already simplified: $7xy$.

Final expression:
$-5x + 3y + 7xy$
Answer: $-5x + 3y + 7xy$

Would you like me to explain any of these steps in further detail or go over similar problems?

5 Related Questions:

1. How do you identify like terms in an expression?
2. What happens when there are no like terms in an expression?
3. How do you handle constants while simplifying expressions?
4. Can you explain how to simplify expressions with multiple variables, like in problem 8?
5. How do coefficients affect combining like terms?

Tip:

Always group similar terms (like variables or constants) together before simplifying to make your work more organized!