To solve the inequality $9x + 9 \geq 5x - 7$, we proceed as follows:

Step 1: Move all terms involving $x$ to one side

Subtract $5x$ from both sides: $9x - 5x + 9 \geq -7$ This simplifies to: $4x + 9 \geq -7$

Step 2: Move the constant term to the other side

Subtract 9 from both sides: $4x \geq -16$

Step 3: Isolate $x$

Divide both sides by 4: $x \geq -4$

Step 4: Write the solution in interval notation

The solution in interval notation is: $[-4, \infty)$

Do you want more details or have any questions?

Here are five related questions that could extend this concept:

1. How would the solution change if the inequality were $9x + 9 > 5x - 7$ instead of $\geq$?
2. What happens if we divide by a negative number when solving inequalities?
3. How would we graph this solution on a number line?
4. Can you explain how interval notation represents a solution on the number line?
5. What is the difference between open and closed intervals in interval notation?

Tip: Always remember to flip the inequality symbol when multiplying or dividing by a negative number.