We are given the equation:

\[
\frac{2}{3}(x + 2) - (x + 4) = 3x + 2
\]

### Step-by-step solution:

1. **Distribute** the \(\frac{2}{3}\) to both terms inside the parentheses:
   \[
   \frac{2}{3}(x + 2) = \frac{2}{3}x + \frac{4}{3}
   \]
   So the equation becomes:
   \[
   \frac{2}{3}x + \frac{4}{3} - (x + 4) = 3x + 2
   \]

2. **Distribute** the negative sign through \((x + 4)\):
   \[
   - (x + 4) = -x - 4
   \]
   Now the equation is:
   \[
   \frac{2}{3}x + \frac{4}{3} - x - 4 = 3x + 2
   \]

3. **Combine like terms** on the left side:
   \[
   \left(\frac{2}{3}x - x\right) + \left(\frac{4}{3} - 4\right) = 3x + 2
   \]
   First, simplify \(\frac{2}{3}x - x\). Recall that \(x = \frac{3}{3}x\), so:
   \[
   \frac{2}{3}x - \frac{3}{3}x = -\frac

Explore how to solve the linear equation 2/3(x+2) - (x+4) = 3x+2 with a comprehensive step-by-step solution. The problem involves algebraic techniques such as the distributive property and combining like terms, suitable for students in Grades 8-10.

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