Let's solve the inequality \( 3 - 2x < 9 \).

### Step 1: Isolate \( x \)
Start by subtracting 3 from both sides:
\[
3 - 2x - 3 < 9 - 3
\]
\[
-2x < 6
\]

### Step 2: Solve for \( x \)
Now, divide both sides by \( -2 \). Remember, when dividing by a negative number, we must reverse the inequality sign:
\[
x > \frac{6}{-2}
\]
\[
x > -3
\]

### Final Inequality:
\[
x > -3
\]

### Graph on a Number Line:
On the number line, \( x > -3 \) means all values to the right of \( -3 \). We represent \( -3 \) with an open circle (since \( x \) is strictly greater than \( -3 \)) and shade the line to the right of \( -3 \).

#### Graph Summary:
- Open circle at \( -3 \)
- Shade all points to the right of \( -3 \)

Would you like me to create a visual graph for this?

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Here are some related questions you might find useful:

1. What happens if you reverse the inequality in similar equations?
2. How do you handle inequalities involving absolute values?
3. How do you solve inequalities with fractions?
4. Can you explain how the graph of a quadratic inequality looks?
5. How do you check if a solution to an inequality is correct?

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

Solve and graph on a number line 3 - 2x < 9

Learn how to solve and graph the linear inequality 3 - 2x < 9 with step-by-step instructions. Understand key concepts like isolating the variable and applying the sign reversal rule. Perfect for students in Grades 7-9.

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