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Let's solve the given equation:

\[
5x + 6 = 9x + 30
\]

### Step-by-step solution:

1. **Move the terms involving \(x\) to one side**:
   Subtract \(5x\) from both sides:
   \[
   5x + 6 - 5x = 9x + 30 - 5x
   \]
   Simplifies to:
   \[
   6 = 4x + 30
   \]

2. **Move the constant terms to the other side**:
   Subtract 30 from both sides:
   \[
   6 - 30 = 4x + 30 - 30
   \]
   Simplifies to:
   \[
   -24 = 4x
   \]

3. **Solve for \(x\)**:
   Divide both sides by 4:
   \[
   \frac{-24}{4} = \frac{4x}{4}
   \]
   Simplifies to:
   \[
   x = -6
   \]

So, the solution is \(x = -6\).

Would you like more details or have any questions?

### Related Questions:
1. What happens if we rearrange the equation in different ways?
2. How can we verify that \(x = -6\) is the correct solution?
3. Can we solve the equation graphically to find \(x\)?
4. What other methods can be used to solve linear equations?
5. How does this equation change if there are fractional terms?

### Tip:
Always double-check your solution by substituting the value of \(x\) back into the original equation to ensure it satisfies the equation.

Learn how to solve the linear equation 5x + 6 = 9x + 30 step by step. This problem involves moving terms, isolating variables, and solving for x. Ideal for students in Grades 6-8, this solution covers core algebraic concepts and methods.

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