Solve AND graph the Solution yo each of the inequalities
 
x
3
>
−
4
x3>−4

We are tasked with solving and graphing the inequality \( \frac{x}{3} > -4 \).

### Step 1: Solve the inequality
To isolate \( x \), we can multiply both sides of the inequality by 3 to eliminate the denominator.

\[
x > -4 \times 3
\]

\[
x > -12
\]

Thus, the solution to the inequality is:

\[
x > -12
\]

### Step 2: Graph the solution
To graph \( x > -12 \) on a number line:

1. Draw a number line.
2. Mark the point \( -12 \) on the line.
3. Use an open circle at \( -12 \) to indicate that \( -12 \) is not included in the solution.
4. Shade the region to the right of \( -12 \), indicating all numbers greater than \( -12 \).

### Graph Explanation:
- The open circle at \( -12 \) represents that \( x = -12 \) is not part of the solution.
- The shaded area to the right represents all values greater than \( -12 \).

Would you like a visual graph for better understanding? Let me know if you have any questions or if you'd like further details.

Here are 5 related questions to expand on this topic:
1. What happens if the inequality was \( x/3 \geq -4 \)?
2. How would the solution change if the inequality was \( x/3 < -4 \)?
3. How would the graph change if the inequality was \( x/3 = -4 \)?
4. What is the solution to \( 2x + 3 > 7 \)?
5. How do you graph inequalities involving absolute values?

**Tip:** Always remember to reverse the inequality sign when multiplying or dividing both sides of an inequality by a negative number.

Solve and graph the solution to each of the inequalities: x/3 > -4

Explore how to solve the inequality x/3 > -4 and learn how to graph the solution on a number line. This tutorial covers key algebraic concepts, including inequality manipulation and graphing on a number line. Perfect for middle school students in Grades 6-8.

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