I can see the inequalities from the image you uploaded. Let me go through each one and solve them step-by-step:

Problem 11: $66 > 2(5x + 3)$

1. Distribute the $2$:
   $66 > 2(5x + 3)$
   $66 > 10x + 6$

2. Subtract 6 from both sides:
   $60 > 10x$

3. Divide by 10:
   $6 > x$
   or
   $x < 6$

Problem 12: $-4x - 5(x + 6) \leq -66$

1. Distribute the $-5$:
   $-4x - 5(x + 6) \leq -66$
   $-4x - 5x - 30 \leq -66$

2. Combine like terms:
   $-9x - 30 \leq -66$

3. Add 30 to both sides:
   $-9x \leq -36$

4. Divide by $-9$ (reverse the inequality):
   $x \geq 4$

Problem 13: $2 + 4(3 - 2x) \geq 6$

1. Distribute the $4$:
   $2 + 12 - 8x \geq 6$

2. Combine like terms:
   $14 - 8x \geq 6$

3. Subtract 14 from both sides:
   $-8x \geq -8$

4. Divide by $-8$ (reverse the inequality):
   $x \leq 1$

Problem 14: $2(2x + 2) + 2(2x + 5) \leq 14$

1. Distribute the $2$ on both terms:
   $4x + 4 + 4x + 10 \leq 14$

2. Combine like terms:
   $8x + 14 \leq 14$

3. Subtract 14 from both sides:
   $8x \leq 0$

4. Divide by 8:
   $x \leq 0$

Would you like a more detailed breakdown or explanation for any of these? Here are 5 related questions to deepen understanding:

1. How do we reverse inequality signs when dividing by a negative number?
2. What is the difference between solving an equation and an inequality?
3. How can we represent these solutions on a number line?
4. What would happen if we change the inequality symbols in these problems?
5. Can inequalities have multiple solutions, and how are they represented?

Tip: Always remember to reverse the inequality sign when you multiply or divide both sides by a negative number.