Let's solve the equation step by step:

The equation is:

\[
6x - \frac{11}{7} = 2x - \frac{9}{3}
\]

### Step 1: Eliminate the fractions
To simplify the equation, let's first get rid of the fractions by multiplying through by 21 (the least common multiple of 7 and 3):

\[
21 \cdot \left(6x - \frac{11}{7}\right) = 21 \cdot \left(2x - \frac{9}{3}\right)
\]

This gives:

\[
21 \cdot 6x - 21 \cdot \frac{11}{7} = 21 \cdot 2x - 21 \cdot \frac{9}{3}
\]

Simplifying each term:

\[
126x - 33 = 42x - 63
\]

### Step 2: Move the terms with \(x\) to one side
Subtract \(42x\) from both sides:

\[
126x - 42x - 33 = -63
\]

This simplifies to:

\[
84x - 33 = -63
\]

### Step 3: Move the constant term to the other side
Add 33 to both sides:

\[
84x = -63 + 33
\]

Simplifying:

\[
84x = -30
\]

### Step 4: Solve for \(x\)
Divide both sides by 84:

\[
x = \frac{-30}{84}
\]

Simplify the fraction:

\[
x = \frac{-5}{14}
\]

Thus, the solution is:

\[
x = \frac{-5}{14}
\]

Would you like further details or clarifications?

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Here are some related questions:
1. How do you solve equations with variables on both sides?
2. What is the least common multiple, and how do you find it?
3. How can you simplify fractions in equations?
4. How do you eliminate fractions in algebraic equations?
5. How do you check if a solution to an equation is correct?

**Tip:** When solving equations, always try to simplify the equation by eliminating fractions early in the process.

Learn how to solve the linear equation 6x - 11/7 = 2x - 9/3 with step-by-step explanations. This algebra problem demonstrates how to eliminate fractions, isolate variables, and simplify equations. Ideal for students in Grades 8-10.

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