https://file.aiquickdraw.com/mathbot/file/1730162789734mmvu7izt.jpg

Let's solve each equation one by one and then match them with the correct answers:

1. \( 4x = 40 \)
   - Divide both sides by 4: \( x = \frac{40}{4} = 10 \)

2. \( x + 5 = 10 \)
   - Subtract 5 from both sides: \( x = 10 - 5 = 5 \)

3. \( x + 8 = 11 \)
   - Subtract 8 from both sides: \( x = 11 - 8 = 3 \)

4. \( x - 11 = 16 \)
   - Add 11 to both sides: \( x = 16 + 11 = 27 \)

5. \( x - 9 = 21 \)
   - Add 9 to both sides: \( x = 21 + 9 = 30 \)

6. \( x + 3 = 32 \)
   - Subtract 3 from both sides: \( x = 32 - 3 = 29 \)

7. \( 6x = 42 \)
   - Divide both sides by 6: \( x = \frac{42}{6} = 7 \)

8. \( x + 14 = 46 \)
   - Subtract 14 from both sides: \( x = 46 - 14 = 32 \)

9. \( 8x = -32 \)
   - Divide both sides by 8: \( x = \frac{-32}{8} = -4 \)

10. \( x + 4 = 64 \)
    - Subtract 4 from both sides: \( x = 64 - 4 = 60 \)

### Solutions and Matching

1. \( x = 10 \)
2. \( x = 5 \)
3. \( x = 3 \)
4. \( x = 27 \)
5. \( x = 30 \)
6. \( x = 29 \)
7. \( x = 7 \)
8. \( x = 32 \)
9. \( x = -4 \)
10. \( x = 60 \)

These match with the given answers:

- \( x = 10 \) for equation 1
- \( x = 5 \) for equation 2
- \( x = 3 \) for equation 3
- \( x = 27 \) for equation 4
- \( x = 30 \) for equation 5
- \( x = 29 \) for equation 6
- \( x = 7 \) for equation 7
- \( x = 32 \) for equation 8
- \( x = -4 \) for equation 9
- \( x = 60 \) for equation 10

Would you like a detailed breakdown of any particular step, or do you have any questions?

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Here are 5 follow-up questions to extend your understanding:

1. How would you solve an equation with variables on both sides?
2. What happens when you have fractions in the equation?
3. Can equations have more than one solution?
4. How do you solve an inequality instead of an equation?
5. How would you check if your solution to an equation is correct?

**Tip:** Always isolate the variable by performing the inverse operations step-by-step.

Solve the following algebraic equations and match each with its result.

Practice solving basic algebraic equations and match each equation with its correct result. This exercise involves simple linear equations, ideal for students in Grades 6-8 to reinforce their algebraic skills.

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