To solve the inequality \(6 + \frac{1}{3}(8 - x) < -8\), follow these steps:

1. **Distribute** the \(\frac{1}{3}\) across the terms inside the parentheses:
   \[
   6 + \frac{1}{3} \times 8 - \frac{1}{3} \times x < -8
   \]
   This simplifies to:
   \[
   6 + \frac{8}{3} - \frac{x}{3} < -8
   \]

2. **Combine the constants** on the left-hand side:
   \[
   \frac{6 \times 3}{3} + \frac{8}{3} - \frac{x}{3} < -8
   \]
   Simplifying the constants:
   \[
   \frac{18}{3} + \frac{8}{3} - \frac{x}{3} < -8
   \]
   \[
   \frac{26}{3} - \frac{x}{3} < -8
   \]

3. **Multiply the entire inequality** by 3 to eliminate the fractions:
   \[
   26 - x < -24
   \]

4. **Isolate** \(x\) by subtracting 26 from both sides:
   \[
   -x < -24 - 26
   \]
   \[
   -x < -50
   \]

5. **Multiply** by \(-1\) (and reverse the inequality):
   \[
   x > 50
   \]

So, the solution is \(x > 50\).

### Do you have any questions or would you like more details on any step?

Here are 5 related questions to explore further:
1. How would the solution change if the inequality was \(6 + \frac{1}{3}(8 - x) > -8\)?
2. What is the graphical representation of the inequality \(x > 50\)?
3. How do you solve a compound inequality like \(6 + \frac{1}{3}(8 - x) < -8 \text{ and } x \leq 55\)?
4. Can you derive the inequality using a different method, such as graphing?
5. How would the inequality change if the fraction was different, say \(\frac{2}{3}\) instead of \(\frac{1}{3}\)?

**Tip:** When solving inequalities, always remember to reverse the inequality sign when you multiply or divide by a negative number.

Learn how to solve the inequality 6 + 1/3(8 - x) < -8 step-by-step with detailed explanations. This problem involves inequalities, the distributive property, and equation solving techniques. Suitable for high school students.

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