It looks like there's a small typo in the equation you've provided. I'll correct it based on what I think you're trying to express.

Let’s assume you meant the following equation:

\[ 6(7x + 9) = 47 \]

Now, I'll solve this step by step.

### Step 1: Distribute the 6
\[
6 \times (7x + 9) = 47
\]
\[
42x + 54 = 47
\]

### Step 2: Isolate the variable term (subtract 54 from both sides)
\[
42x + 54 - 54 = 47 - 54
\]
\[
42x = -7
\]

### Step 3: Solve for \( x \) (divide both sides by 42)
\[
x = \frac{-7}{42}
\]
\[
x = -\frac{1}{6}
\]

### Final Answer:
\[
x = -\frac{1}{6}
\]

Would you like more details, or have any questions?

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Here are 5 follow-up questions to test your understanding:
1. Can you solve \( 5(3x + 2) = 30 \)?
2. What happens if you change \( 47 \) to \( 57 \) in the original equation?
3. How would you solve the equation if there were two terms with \( x \)?
4. What is the significance of distributing in equations?
5. What are the next steps if the equation had fractions?

**Tip:** Always distribute any constants outside parentheses before moving terms to isolate variables.

Learn how to solve the linear equation 6(7x + 9) = 47 with a detailed step-by-step solution. This problem demonstrates the use of the distributive property and basic algebraic principles to isolate and solve for x. Suitable for students in Grades 6-8.

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