https://file.aiquickdraw.com/mathbot/file/1726103675161gygxgsy6.jpg

The equation in the image is:

\[
w = \frac{x}{y} - z
\]

We need to solve for \(x\). Here's the process:

### Step-by-Step Solution:

1. Start with the original equation:
   \[
   w = \frac{x}{y} - z
   \]

2. Add \(z\) to both sides to move it to the left-hand side:
   \[
   w + z = \frac{x}{y}
   \]

3. Multiply both sides by \(y\) to isolate \(x\) on the right-hand side:
   \[
   y(w + z) = x
   \]

Thus, the solution for \(x\) is:
\[
x = y(w + z)
\]

Would you like any further details or explanations?

### 5 Related Questions:
1. What happens if you solve for \(y\) instead of \(x\) in this equation?
2. How do you solve if the equation involved a quadratic term like \(x^2\)?
3. What if the equation had a coefficient in front of \(x\), such as \(w = \frac{3x}{y} - z\)?
4. How does this method change if you want to solve for \(z\) instead?
5. How can this be extended if the equation had more terms, like \(w = \frac{x}{y} - z + k\)?

### Tip:
Always remember to check for any restrictions in variables (like \(y \neq 0\)) when manipulating algebraic equations!

Learn how to solve the equation w = x/y - z for the variable x with a step-by-step algebraic solution. This problem demonstrates key algebraic concepts like equation manipulation, suitable for students in Grades 9-11.

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