Let's solve the inequality step by step. The inequality in the image is:

$-4b - 9 > -5$

Step 1: Simplify the inequality

Add 9 to both sides to isolate the term with $b$: $-4b - 9 + 9 > -5 + 9$ $-4b > 4$

Step 2: Solve for $b$

Divide both sides by $-4$. Remember, dividing or multiplying an inequality by a negative number reverses the inequality sign: $b < \frac{4}{-4}$ $b < -1$

Final Answer:

$b < -1$

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Would you like further details or explanations? Let me know!

Follow-Up Questions:

1. Why does the inequality sign reverse when dividing by a negative number?
2. How can you check if a value satisfies the inequality $b < -1$?
3. Can you graph $b < -1$ on a number line? What does it look like?
4. How would the solution change if the inequality were $-4b - 9 \geq -5$?
5. How does solving an inequality differ from solving an equation?

Tip:

Always remember to reverse the inequality sign when multiplying or dividing by a negative number!