Let's solve the inequality step by step:

Given:
\[
-5h - (h + 2) \geq 5h + 8 + 6
\]

### Step 1: Distribute and simplify the terms

Distribute the negative sign on the left side:
\[
-5h - h - 2 \geq 5h + 8 + 6
\]

Combine like terms on both sides:
\[
-6h - 2 \geq 5h + 14
\]

### Step 2: Move all terms involving \( h \) to one side

Add \( 6h \) to both sides to isolate \( h \):
\[
-2 \geq 11h + 14
\]

### Step 3: Move constant terms to the other side

Subtract 14 from both sides:
\[
-2 - 14 \geq 11h
\]

Simplify:
\[
-16 \geq 11h
\]

### Step 4: Solve for \( h \)

Divide both sides by 11:
\[
h \leq -\frac{16}{11}
\]

### Conclusion

The solution to the inequality is:
\[
h \leq -\frac{16}{11}
\]

This means \( h \) must be less than or equal to \(-\frac{16}{11}\).

### Would you like more details or have any questions?

Here are 5 related questions to expand your understanding:

1. How do you solve inequalities that involve fractions?
2. What happens to an inequality sign when you multiply or divide by a negative number?
3. How can inequalities be represented on a number line?
4. What are some real-life applications of solving inequalities?
5. How do compound inequalities differ from simple inequalities?

**Tip:** Always check your solution by substituting back into the original inequality.

Learn how to solve the inequality -5h - (h + 2) ≥ 5h + 8 + 6 with a detailed step-by-step solution. This problem covers solving inequalities, the distributive property, and simplifying algebraic expressions. Suitable for students in Grades 9-12.

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