https://file.aiquickdraw.com/mathbot/file/1726183871426bflxg4rp.jpg

I've reviewed the image you uploaded, which contains problems related to solving complex one-variable equations from a Grade 8 math book (Spectrum Math, Chapter 3, Lesson 4). It seems that some equations have already been solved and answers are written next to them. Let’s go through a few of them to ensure the solutions are correct.

Here are the equations and their solutions based on the image:

1. **Equation 1:** \( x + 5 = 10 \)
   - Solution: \( x = 5 \) (correct)

2. **Equation 2:** \( \frac{6x}{9} = 5 \)
   - Solution: \( x = 7.5 \) (the given answer is 6, which is incorrect; correct answer should be \( x = 7.5 \))

3. **Equation 3:** \( 5x - 4 = 11 \)
   - Solution: \( x = 3 \) (correct)

4. **Equation 4:** \( 3x - 9 = -3 \)
   - Solution: \( x = 2 \) (correct)

5. **Equation 5:** \( 2x + 12 = 14 \)
   - Solution: \( x = 1 \) (correct)

Some answers appear to be incorrect or need revising. Let me know if you want me to go over specific problems or verify other answers.

Would you like me to explain any particular solutions or provide more detailed steps?

Here are some related questions that might help further your understanding:

1. How do you solve linear equations with variables on both sides?
2. What methods can you use to verify your solutions to equations?
3. How do you handle equations that involve fractions?
4. What are common mistakes to watch out for when solving one-variable equations?
5. How can you apply these skills to real-world problems involving equations?

**Tip:** Always double-check your steps by substituting the solution back into the original equation to ensure it satisfies the equation.

Find the value of the variable in each equation (as shown in the image from the Spectrum Math book, Chapter 3, Lesson 4).

Explore how to solve one-variable linear equations step by step using properties of equality. Suitable for students in Grade 8, this lesson covers methods for solving equations like 5x - 4 = 11 and 3y + 9 = 6. The concepts focus on isolating the variable, including equations with fractions.

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