The given equation is:

\[
\frac{7}{2} \left(14x + \frac{2}{7}\right) - 3x = 9
\]

Let's solve it step by step.

### Step 1: Distribute \(\frac{7}{2}\) inside the parentheses

\[
\frac{7}{2} \times 14x + \frac{7}{2} \times \frac{2}{7}
\]

This simplifies to:

\[
49x + 1
\]

So the equation now becomes:

\[
49x + 1 - 3x = 9
\]

### Step 2: Combine like terms

\[
(49x - 3x) + 1 = 9
\]

This simplifies to:

\[
46x + 1 = 9
\]

### Step 3: Subtract 1 from both sides

\[
46x = 8
\]

### Step 4: Divide both sides by 46

\[
x = \frac{8}{46}
\]

Simplify the fraction:

\[
x = \frac{4}{23}
\]

So, the solution is:

\[
\boxed{x = \frac{4}{23}}
\]

Would you like more details on any step, or do you have any questions? Here are some related questions you might find interesting:

1. How do you solve linear equations involving fractions?
2. What are some techniques for simplifying fractions?
3. How do you solve equations with variables on both sides?
4. How do you handle equations that involve distribution?
5. What are common mistakes to avoid when solving linear equations?

**Tip:** When solving equations with fractions, it can be helpful to first eliminate the fractions by multiplying by the least common denominator (LCD).

Learn how to solve the equation (14x + 2/7) - 3x = 9 with a detailed step-by-step solution. This problem covers key algebraic concepts, including equations, the distributive property, and solving linear equations. Suitable for students in Grades 7-9.

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