9>−3−4x?
I., 3, II., minus, 11, III., minus, 3
I.3II.−11III.−3

The expression given is:

\[
9 > -3 - 4x
\]

We need to solve this inequality for \( x \).

### Step 1: Isolate the term with \( x \)
First, add 3 to both sides to begin isolating the \( x \) term:

\[
9 + 3 > -4x
\]

Simplifying:

\[
12 > -4x
\]

### Step 2: Solve for \( x \)
Next, divide both sides by \(-4\). Remember, when you divide or multiply both sides of an inequality by a negative number, the inequality sign flips:

\[
\frac{12}{-4} < x
\]

This simplifies to:

\[
-3 < x
\]

Or, written in standard form:

\[
x > -3
\]

### Final Answer
The solution to the inequality is \( x > -3 \).

This solution matches the context of the options provided:

- **I. 3**: Incorrect, as \( x > -3 \), not \( x > 3 \).
- **II. -11**: Incorrect.
- **III. -3**: Partially correct, but the exact solution is \( x > -3 \), not \( x = -3 \).

### Relative Questions:
1. What happens to the inequality sign when you multiply or divide both sides by a negative number?
2. How would the solution change if the inequality were \( 9 < -3 - 4x \)?
3. Can inequalities have more than one solution? If so, how?
4. How can you graph the solution \( x > -3 \) on a number line?
5. What is the difference between solving an inequality and solving an equation?

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

Discover how to solve the inequality 9 > -3 - 4x with a step-by-step breakdown. This solution covers essential algebra concepts, focusing on inequality manipulation and the division rule for inequalities. Perfect for students in Grades 7-9.

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