To solve the equation \(6r - 3 = 9r - 6\), we will first isolate the variable \(r\) on one side. Here are the steps:

1. **Subtract \(6r\) from both sides** to start simplifying:

\[
6r - 3 - 6r = 9r - 6 - 6r
\]

This simplifies to:

\[
-3 = 3r - 6
\]

2. **Add 6 to both sides** to further isolate terms involving \(r\):

\[
-3 + 6 = 3r - 6 + 6
\]

This simplifies to:

\[
3 = 3r
\]

3. **Divide by 3** to solve for \(r\):

\[
\frac{3}{3} = \frac{3r}{3}
\]

This gives:

\[
r = 1
\]

### Final Answer:
\(r = 1\)

Would you like more details, or do you have any other questions?

### Related Questions:
1. How do you solve equations with variables on both sides?
2. What are the different methods to solve linear equations?
3. How do you check if your solution to an equation is correct?
4. Can you solve an equation with fractions involved?
5. What happens if an equation has no solution or infinite solutions?

**Tip:** Always perform the same operation on both sides of the equation to keep it balanced.

Learn how to solve the linear equation 6r - 3 = 9r - 6 step-by-step. This problem covers key algebraic concepts like isolating variables, simplifying both sides, and using properties of equality. Suitable for students in Grades 6-8.

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