https://file.aiquickdraw.com/mathbot/file/1726718211686wdemgr3q.jpg

The equations shown in the image appear to be the following:

1. \( K + x = w - v + yx \)
2. Then, rearranged:
   \[
   x = -K + w - v + yx
   \]
3. Lastly:
   \[
   x = -K + w - v(1 + y)
   \]

Let me solve the equation systematically.

1. **Starting with** \( K + x = w - v + yx \):

   - We want to isolate \( x \). Move all terms involving \( x \) to one side:
     \[
     x - yx = w - v - K
     \]
   
   - Factor out \( x \) on the left side:
     \[
     x(1 - y) = w - v - K
     \]

   - Solve for \( x \):
     \[
     x = \frac{w - v - K}{1 - y}
     \]

This is the final form of \( x \).

Would you like more details or have any questions? Here are some related problems to deepen your understanding:

1. What happens if \( y = 1 \) in the solution?
2. How would the solution change if \( K \) were negative?
3. Can this equation be solved graphically? What would the graph look like?
4. What if you had more variables on the right-hand side (e.g., \( w = z \))?
5. How does this equation behave if \( y \) is very close to 1?

**Tip**: When solving algebraic equations, always try to factor or group similar terms to simplify the process.

Solve for x in the equation K + x = w - v + yx.

Learn how to solve the linear equation K + x = w - v + yx using algebraic manipulation. This step-by-step solution covers essential algebraic concepts like isolating variables and rearranging equations. Suitable for high school students (Grades 9-12).

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