Let's solve the equation for \( x \):

\[
\frac{1}{3}(5x - 9) + 2 = 12x + \frac{2}{3}
\]

### Step 1: Eliminate the fractions by multiplying the entire equation by 3:
\[
3 \times \left( \frac{1}{3}(5x - 9) + 2 \right) = 3 \times \left( 12x + \frac{2}{3} \right)
\]

This simplifies to:
\[
(5x - 9) + 6 = 36x + 2
\]

### Step 2: Simplify both sides of the equation:
\[
5x - 9 + 6 = 36x + 2
\]
\[
5x - 3 = 36x + 2
\]

### Step 3: Move all terms involving \( x \) to one side and constant terms to the other:
\[
5x - 36x = 2 + 3
\]
\[
-31x = 5
\]

### Step 4: Solve for \( x \):
\[
x = \frac{5}{-31}
\]
\[
x = -\frac{5}{31}
\]

Thus, the solution is:
\[
x = -\frac{5}{31}
\]

Do you have any questions, or would you like further details?

Here are 5 related questions to explore:

1. How would the solution change if the constant term on the right side were different?
2. Can you solve a similar equation with a different fractional coefficient?
3. What is the process for solving equations with more than one fraction?
4. How do you verify that your solution is correct?
5. What happens if we introduce additional variables to both sides of the equation?

**Tip**: When working with fractions, it can often be easier to eliminate them early by multiplying both sides by a common denominator.

Discover how to solve the linear equation 1/3(5x-9) + 2 = 12x + 2/3. This step-by-step solution covers essential algebraic methods such as eliminating fractions, simplifying equations, and solving for x. Suitable for students in Grades 8-10.

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