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The inequality given is:

\[
\frac{-22 - x}{5} - 2 \geq -7
\]

### Step-by-step solution:

1. **Start by isolating the term with the fraction:**
   Add 2 to both sides to eliminate the constant term on the left:
   \[
   \frac{-22 - x}{5} \geq -7 + 2
   \]
   \[
   \frac{-22 - x}{5} \geq -5
   \]

2. **Multiply both sides by 5** to eliminate the denominator:
   \[
   -22 - x \geq -5 \times 5
   \]
   \[
   -22 - x \geq -25
   \]

3. **Isolate \(x\):** Add 22 to both sides:
   \[
   -x \geq -25 + 22
   \]
   \[
   -x \geq -3
   \]

4. **Multiply through by \(-1\)** to get rid of the negative sign. Remember to **reverse the inequality** when multiplying by a negative number:
   \[
   x \leq 3
   \]

### Final Solution:
\[
x \leq 3
\]

Would you like more details or have any questions?

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Here are five related questions:
1. How would the solution change if the inequality were strict (i.e., \( > \) instead of \( \geq \))?
2. Can you solve this inequality graphically and compare the solution?
3. What would happen if the inequality involved division by a negative number?
4. How does solving inequalities differ from solving equalities?
5. What is the impact of reversing the inequality when multiplying or dividing by negative numbers?

**Tip:** Always remember to reverse the inequality sign when multiplying or dividing by a negative number in an inequality.

Consider the inequality (-22 - x)/5 - 2 ≥ -7.

Solve the inequality (-22 - x)/5 - 2 ≥ -7 step-by-step. Learn how to handle inequalities involving fractions and understand why multiplying or dividing by negative numbers requires reversing the inequality sign. This problem covers core algebraic concepts suitable for Grades 8-10.

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