Let's solve the problem by testing each inequality with $m = 9$.

The inequalities are:

1. $m + 5 < 7$
2. $-m + 5 > 7$
3. $-m + 5 < -7$
4. $-m + 5 < 7$

Now, substitute $m = 9$ into each inequality:

1. $9 + 5 < 7$ $14 < 7 \quad \text{(False)}$

2. $-9 + 5 > 7$ $-4 > 7 \quad \text{(False)}$

3. $-9 + 5 < -7$ $-4 < -7 \quad \text{(False)}$

4. $-9 + 5 < 7$ $-4 < 7 \quad \text{(True)}$

So, the correct inequality is the last one: $-m + 5 < 7$.

Would you like more details or have any other questions?

Here are five related questions for further practice:

1. What is the solution to $m - 4 > 10$?
2. How do you solve inequalities involving absolute values?
3. How can you graph the solution of $x + 2 \leq 5$?
4. What happens to the inequality sign when both sides are multiplied by a negative number?
5. How can inequalities be used to solve real-world problems?

Tip: Always check your inequality solution by substituting values into the original equation to ensure it holds true.