To simplify the expression \(3x + 2x - \frac{4}{3} - \frac{x}{2}\), let's combine like terms and simplify step-by-step.

### Step-by-Step Simplification:

1. **Combine like terms involving \(x\):**

   \[
   3x + 2x = 5x
   \]

2. **Rewrite the expression with the combined terms:**

   \[
   5x - \frac{4}{3} - \frac{x}{2}
   \]

3. **Combine the fractions:**

   To combine the fractions, we need a common denominator. The denominators are 3 and 2, so the least common denominator (LCD) is 6.

   \[
   5x - \left(\frac{4}{3} \cdot \frac{2}{2}\right) - \left(\frac{x}{2} \cdot \frac{3}{3}\right)
   \]

4. **Convert the fractions to have a common denominator:**

   \[
   5x - \frac{8}{6} - \frac{3x}{6}
   \]

5. **Combine the terms over the common denominator:**

   Since we only have one fraction, let's rewrite the expression as:

   \[
   5x - \frac{3x + 8}{6}
   \]

6. **Distribute and simplify further:**

   \[
   5x - \frac{3x}{6} - \frac{8}{6}
   \]

   Simplify the coefficients:

   \[
   5x - \frac{x}{2} - \frac{4}{3}
   \]

   Which gives us:

   \[
   \frac{10x - 3x - 8}{6} = \frac{7x - 8}{6}
   \]

### Final Simplified Expression:

\[
\frac{7x - 8}{6}
\]

Would you like more details on any of these steps, or do you have any questions?

### Related Questions:

1. How do you find the least common denominator for fractions?
2. What are like terms in algebra, and how do you combine them?
3. How do you simplify algebraic expressions involving fractions?
4. What is the difference between simplifying and factoring expressions?
5. How can you solve an equation after simplifying it?

**Tip:** Always ensure that all terms are fully simplified and combined where possible for a cleaner final expression!

Learn how to simplify the algebraic expression 3x + 2x - 4/3 - x/2 step-by-step with detailed explanations and examples. This problem covers key algebraic concepts such as combining like terms and operations with fractions. Suitable for students in Grades 7-9.

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