Let's solve the given expression step by step:

\[
(-5x/3 + 3x/2 + 8x + 6) + (3x/3 - 2x/2 - 11x)
\]

### Step 1: Simplify each term
1. **Simplify** the fractions where possible:
   - \( -5x/3 \) stays as is.
   - \( 3x/2 \) stays as is.
   - \( 8x \) stays as is.
   - \( 6 \) stays as is (constant term).
   - \( 3x/3 = x \).
   - \( -2x/2 = -x \).
   - \( -11x \) stays as is.

Now the expression becomes:

\[
(-5x/3 + 3x/2 + 8x + 6) + (x - x - 11x)
\]

### Step 2: Combine like terms
Let's combine all the \( x \)-terms together:
\[
(-5x/3 + 3x/2 + 8x) + (x - x - 11x)
\]

The terms involving \( x \) are:
- \( -5x/3 \)
- \( +3x/2 \)
- \( +8x \)
- \( +x \)
- \( -x \)
- \( -11x \)

### Step 3: Add the constant term
The constant term is just \( +6 \).

### Step 4: Find the common denominator
To combine the fractional terms, we find the common denominator for \( -5x/3 \) and \( 3x/2 \). The least common denominator (LCD) between 3 and 2 is 6. We rewrite the fractions:

\[
-5x/3 = -10x/6 \quad \text{and} \quad 3x/2 = 9x/6
\]

Now, the \( x \)-terms are:

\[
-10x/6 + 9x/6 + 8x - 11x
\]

### Step 5: Combine all terms
Now, we combine all the terms:
\[
\left( \frac{-10x + 9x}{6} \right) + (8x - 11x) = \frac{-x}{6} + (-3x)
\]

### Final expression:
Now simplify:
\[
\frac{-x}{6} - 3x + 6
\]

This is the simplified form of the given expression.

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Do you want more details or have any questions?

Here are 5 related questions to explore further:
1. How do you combine fractional terms with different denominators?
2. What is the importance of finding the least common denominator?
3. How do you simplify expressions with multiple variables?
4. What strategies are useful for solving equations involving fractions?
5. How do you handle constant terms in algebraic expressions?

**Tip:** Always simplify terms with fractions by finding a common denominator to avoid errors.

Explore how to simplify algebraic expressions involving fractions with a step-by-step solution for (-5x/3 + 3x/2 + 8x + 6) + (3x/3 - 2x/2 - 11x). This tutorial covers combining like terms and working with fractions, ideal for Grades 8-10.

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