https://file.aiquickdraw.com/mathbot/file/1727307765677hpm7rimn.jpg

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  
   \( x < 6 \)

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### 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):  
   \( x \geq 4 \)

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### 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):  
   \( x \leq 1 \)

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### 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:  
   \( x \leq 0 \)

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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.

Solve the following inequalities: 1) 66 > 2(5x + 3), 2) -4x - 5(x + 6) <= -66, 3) 2 + 4(3 - 2x) >= 6, 4) 2(2x + 2) + 2(2x + 5) <= 14

This page provides step-by-step solutions to four algebraic inequalities, including the use of the distributive property, combining like terms, and solving inequalities. Suitable for students in Grades 8-10. Learn how to solve inequalities like 66 > 2(5x + 3) and others.

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