To solve the inequality \( -4m + 5 < 2(-2 - m) \), follow these steps:

1. **Distribute the 2 on the right-hand side**:
   \[
   -4m + 5 < 2(-2) + 2(-m)
   \]
   \[
   -4m + 5 < -4 - 2m
   \]

2. **Move all terms involving \( m \) to one side** and constant terms to the other side. Add \( 2m \) to both sides:
   \[
   -4m + 2m + 5 < -4
   \]
   \[
   -2m + 5 < -4
   \]

3. **Subtract 5 from both sides** to isolate the term with \( m \):
   \[
   -2m < -4 - 5
   \]
   \[
   -2m < -9
   \]

4. **Divide both sides by -2**, and remember to **reverse the inequality sign** because you're dividing by a negative number:
   \[
   m > \frac{-9}{-2}
   \]
   \[
   m > 4.5
   \]

So, the solution is \( m > 4.5 \).

Would you like any more details or have questions?

Here are five related questions:
1. How do you solve inequalities with fractions?
2. What happens when you multiply or divide both sides of an inequality by a negative number?
3. How do you solve compound inequalities?
4. What is the difference between solving equations and inequalities?
5. How do you graph the solution to an inequality on a number line?

**Tip:** Always remember to reverse the inequality sign when you multiply or divide by a negative number.

Learn how to solve the inequality -4m + 5 < 2(-2 - m) with detailed steps and explanations. This problem involves inequalities, the distributive property, and solving linear inequalities. Suitable for students in Grades 7-9.

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