To solve the equation \( ax - 3b = 2x \) for \(x\), follow these steps:

1. Move all terms involving \(x\) to one side of the equation:
\[
ax - 2x = 3b
\]
2. Factor out \(x\) from the left-hand side:
\[
x(a - 2) = 3b
\]
3. Solve for \(x\):
\[
x = \frac{3b}{a - 2}
\]

So, the solution is:
\[
x = \frac{3b}{a - 2}
\]

Would you like more details or have any questions? 

Here are some related questions to expand on this:
1. What happens if \(a = 2\) in this equation?
2. How does factoring work when solving linear equations?
3. How do you isolate a variable in an equation?
4. What are the implications of the denominator in the solution?
5. Can this equation have no solution?

**Tip:** Always check for any values that make the denominator zero to avoid undefined expressions.

Learn how to solve the linear equation ax - 3b = 2x by isolating the variable x. This problem covers key algebraic concepts, including solving for variables and factoring. Suitable for students in Grades 9-12.

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