The equation you provided is:

\[
ax - bx = c
\]

### Solution:

1. Combine like terms on the left-hand side:

\[
(ax - bx) = (a - b)x
\]

2. This simplifies to:

\[
(a - b)x = c
\]

3. To solve for \(x\), divide both sides of the equation by \((a - b)\) (assuming \(a \neq b\)):

\[
x = \frac{c}{a - b}
\]

So, the solution for \(x\) is:

\[
x = \frac{c}{a - b}
\]

---

Would you like further details or have any questions?

### Related questions:
1. How does this equation change if \(a = b\)?
2. What happens if \(c = 0\)?
3. How can this be applied to a system of equations?
4. What is the graphical interpretation of this equation?
5. Can you derive other forms of the solution by manipulating the equation?

### Tip: 
Always check for cases where the denominator becomes zero, as it could lead to undefined solutions.

Learn how to solve the linear equation ax - bx = c with a detailed step-by-step approach. This problem involves key algebraic concepts like combining like terms and solving equations by division. Suitable for students in Grades 8-10.

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