Here are the solutions to the inequalities in the uploaded image:

6) Solve:

$10 - 3(-5b - 6) \leq -9b - 5 + 8$

1. Expand the terms:
   $10 + 15b + 18 \leq -9b + 3$

2. Combine like terms:
   $28 + 15b \leq -9b + 3$

3. Add $9b$ to both sides:
   $28 + 24b \leq 3$

4. Subtract 28 from both sides:
   $24b \leq -25$

5. Divide by 24:
   $b \leq -\frac{25}{24}$

7) Solve:

$3q - (5q + 1) > -5q - 7 - 5q$

1. Expand the terms:
   $3q - 5q - 1 > -10q - 7$

2. Combine like terms:
   $-2q - 1 > -10q - 7$

3. Add $10q$ to both sides:
   $8q - 1 > -7$

4. Add 1 to both sides:
   $8q > -6$

5. Divide by 8:
   $q > -\frac{3}{4}$

8) Solve:

$-5n + 2(-3n - 1) \geq n - 9 + 5n$

1. Expand the terms:
   $-5n - 6n - 2 \geq n - 9 + 5n$

2. Combine like terms:
   $-11n - 2 \geq 6n - 9$

3. Subtract $6n$ from both sides:
   $-17n - 2 \geq -9$

4. Add 2 to both sides:
   $-17n \geq -7$

5. Divide by $-17$ (flip the inequality):
   $n \leq \frac{7}{17}$

9) Solve:

$7 + 5(-4k - 10) > -9k + 2 - 8$

1. Expand the terms:
   $7 - 20k - 50 > -9k - 6$

2. Combine like terms:
   $-20k - 43 > -9k - 6$

3. Add $9k$ to both sides:
   $-11k - 43 > -6$

4. Add 43 to both sides:
   $-11k > 37$

5. Divide by $-11$ (flip the inequality):
   $k < -\frac{37}{11}$

10) Solve:

$6v - 5(8v - 8) < 7v - 7 - 10v$

1. Expand the terms:
   $6v - 40v + 40 < 7v - 7 - 10v$

2. Combine like terms:
   $-34v + 40 < -3v - 7$

3. Add $34v$ to both sides:
   $40 < 31v - 7$

4. Add 7 to both sides:
   $47 < 31v$

5. Divide by 31:
   $v > \frac{47}{31}$

Let me know if you'd like further clarifications or have additional questions!

Related Questions:

1. How do you determine when to flip the inequality sign?
2. Can you explain how combining like terms works in inequalities?
3. What is the process for checking solutions in inequalities?
4. How are these inequalities represented graphically?
5. What happens when dividing both sides by a variable?

Tip:

Always simplify expressions fully before solving inequalities for a cleaner solution path!