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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:
\[
[-4, \infty)
\]

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Do you want more details or have any questions?

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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.

Solve: 9x + 9 ≥ 5x - 7. Enter the exact answer in interval notation.

Learn how to solve the inequality 9x + 9 ≥ 5x - 7 step-by-step, and express the solution in interval notation. This problem involves key algebraic concepts such as inequality manipulation and interval notation, making it suitable for students in Grades 8-10.

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