https://file.aiquickdraw.com/mathbot/file/1729790501935a99o6n62.jpg

https://file.aiquickdraw.com/mathbot/file/1729790501936olkory6u.jpg

Let's solve the equations from the images you uploaded. I will first extract and solve the equations from both images.

### Image 1: Solving for \( x \)

1. \( x - y = w \)
   - Solving for \( x \): 
     \[
     x = y + w
     \]

2. \( \frac{x}{v - w} = y \)
   - Solving for \( x \):
     \[
     x = y(v - w)
     \]

3. \( x + 6y = 3v \)
   - Solving for \( x \):
     \[
     x = 3v - 6y
     \]

4. \( \frac{v}{9x} = \frac{w}{y} \)
   - Solving for \( x \):
     \[
     x = \frac{9vy}{w}
     \]

5. \( x + v = w \)
   - Solving for \( x \):
     \[
     x = w - v
     \]

6. \( vx - w = 2 \)
   - Solving for \( x \):
     \[
     x = \frac{w + 2}{v}
     \]

7. \( 3v + x = w \)
   - Solving for \( x \):
     \[
     x = w - 3v
     \]

8. \( 6w + vx = y \)
   - Solving for \( x \):
     \[
     x = \frac{y - 6w}{v}
     \]

### Image 2: Solving for \( x \)

1. \( a(x + b) = c \)
   - Solving for \( x \):
     \[
     x = \frac{c}{a} - b
     \]
   
2. \( 2(x + a) = b \)
   - Solving for \( x \):
     \[
     x = \frac{b}{2} - a
     \]

3. \( a(x - 2) = b \)
   - Solving for \( x \):
     \[
     x = \frac{b}{a} + 2
     \]

4. \( c(9 + x) = 6 \)
   - Solving for \( x \):
     \[
     x = \frac{6}{c} - 9
     \]

Would you like more details on any specific steps or solutions?

### Related Questions:
1. How can I simplify more complex equations with multiple variables?
2. What happens when there are no real solutions to an equation?
3. Can you solve equations involving exponents for \( x \)?
4. How do you isolate \( x \) in an equation with a fraction?
5. What if \( x \) appears in the denominator? How can I solve for it?

**Tip:** Always try to move all terms involving \( x \) to one side of the equation and constants to the other to simplify the solving process!

Learn how to solve various linear and fractional equations for x with detailed solutions, covering algebraic concepts like isolating variables, cross-multiplication, and simplifying terms. Suitable for students in Grades 8-10.

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