https://file.aiquickdraw.com/mathbot/file/1728710469148n0dh8d0q.jpg

Let's go through the equations in the image and solve them one by one:

1. **\( x + 2 = 0 \)**  
   Solve:  
   \( x = -2 \)

2. **\( 5x = 15 \)**  
   Solve:  
   \( x = \frac{15}{5} = 3 \)

3. **\( -3x = 24 \)**  
   Solve:  
   \( x = \frac{24}{-3} = -8 \)

4. **\( -2x = -10 \)**  
   Solve:  
   \( x = \frac{-10}{-2} = 5 \)

5. **\( 2x = \frac{3}{5} \)**  
   Solve:  
   \( x = \frac{3}{5} \times \frac{1}{2} = \frac{3}{10} \)

6. **\( 2x - 4 = 0 \)**  
   Solve:  
   \( 2x = 4 \),  
   \( x = \frac{4}{2} = 2 \)

7. **\( 6 - 2x = 0 \)**  
   Solve:  
   \( -2x = -6 \),  
   \( x = 3 \)

8. **\( 2x + 1 = 8 \)**  
   Solve:  
   \( 2x = 7 \),  
   \( x = \frac{7}{2} = 3.5 \)

9. **\( x + 1 = 3x + 5 \)**  
   Solve:  
   \( x - 3x = 5 - 1 \),  
   \( -2x = 4 \),  
   \( x = \frac{4}{-2} = -2 \)

10. **\( 3x - 1 = x + 3 \)**  
    Solve:  
    \( 3x - x = 3 + 1 \),  
    \( 2x = 4 \),  
    \( x = 2 \)

11. **\( 2x + 2 = 3x - 4 \)**  
    Solve:  
    \( 2x - 3x = -4 - 2 \),  
    \( -x = -6 \),  
    \( x = 6 \)

12. **\( 3x - 6 = -x - 2 \)**  
    Solve:  
    \( 3x + x = -2 + 6 \),  
    \( 4x = 4 \),  
    \( x = 1 \)

13. **\( x + 10 = 6x - 7 \)**  
    Solve:  
    \( x - 6x = -7 - 10 \),  
    \( -5x = -17 \),  
    \( x = \frac{17}{5} \)

14. **\( -5x + 4 = 10x + 2 \)**  
    Solve:  
    \( -5x - 10x = 2 - 4 \),  
    \( -15x = -2 \),  
    \( x = \frac{-2}{-15} = \frac{2}{15} \)

15. **\( 5 - 2x + 4y = 10x + 2y - 3 \)**  
    Rearrange:  
    \( -2x - 10x + 4y - 2y = -3 - 5 \),  
    \( -12x + 2y = -8 \),  
    Divide by -2:  
    \( 6x - y = 4 \), which is a simplified linear equation in two variables.

16. **\( \frac{3x}{5} = 4 \)**  
    Solve:  
    \( 3x = 4 \times 5 = 20 \),  
    \( x = \frac{20}{3} \)

Would you like details on any specific equation or further explanation?

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**Relative questions**:
1. How do you solve linear equations with one variable?
2. Can you explain how to deal with equations involving fractions?
3. What is the method to solve equations with two variables like in question 15?
4. What happens when both sides of an equation have variables, like in question 9?
5. How do you handle equations that involve multiple terms on both sides?

**Tip**: Always move terms with variables to one side and constants to the other when solving linear equations.

Solve the following algebraic equations (both linear and with fractions) provided in the image.

Learn how to solve various linear equations, including those with fractions and multiple variables, from the provided image. This step-by-step guide covers essential algebraic techniques for Grades 7-10.

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