https://file.aiquickdraw.com/mathbot/file/1734544100775rnsoneul.jpg

Let's solve the inequality \( 2x + 5 < 11 \) step by step:

### Step 1: Isolate \( x \)
Start by subtracting \( 5 \) from both sides:
\[
2x + 5 - 5 < 11 - 5 \quad \Rightarrow \quad 2x < 6
\]

### Step 2: Solve for \( x \)
Divide both sides by \( 2 \) to isolate \( x \):
\[
\frac{2x}{2} < \frac{6}{2} \quad \Rightarrow \quad x < 3
\]

### Step 3: Analyze the solution
The inequality \( x < 3 \) means all values of \( x \) less than \( 3 \) are included. On a number line:
- The point at \( 3 \) is an **open circle** (not included).
- The shading or solution extends to the **left of \( 3 \)**.

### Step 4: Compare to the answer choices
- **Option A**: Shows an open circle at \( 3 \) with shading to the left.  
- **Option B**: Open circle at \( 3 \) with shading to the right.  
- **Option C**: Open circle at \( 8 \) with shading to the left.  
- **Option D**: Open circle at \( 8 \) with shading to the right.  

### Correct Answer:
The solution matches **Option A**.

---

### Do you want further clarification or a breakdown of a specific step?  
Here are 5 related questions to expand on this topic:  
1. How do you solve and graph \( 3x - 7 > 5 \) on a number line?  
2. What is the difference between open and closed circles on a graph?  
3. How do you handle inequalities involving division by a negative number?  
4. Can you explain compound inequalities like \( 2 < x + 1 \leq 5 \)?  
5. How do you check if a solution satisfies an inequality?  

**Tip:** Always check your solution by substituting values into the original inequality!

Which number line shows the solution to the inequality 2x + 5 < 11?

Learn how to solve and graph the inequality 2x + 5 < 11. Follow a step-by-step breakdown to isolate x and represent the solution on a number line. Suitable for students in Grades 6-8.

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