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?

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.