https://file.aiquickdraw.com/mathbot/file/1729016190238lqatkong.jpg

Let's solve the inequality step by step:

**Inequality:**
\[
2x + 5 > 11
\]

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

### Step 2: Solve for \(x\) by dividing both sides by 2:
\[
x > \frac{6}{2}
\]
\[
x > 3
\]

### Solution:
The solution to the inequality is \(x > 3\).

### Graphing the solution:
- The graph should have an open circle at \(x = 3\) (because it is strictly greater than 3, not greater than or equal to).
- The arrow should point to the right, indicating values greater than 3.

### Conclusion:
The correct graph should have an open circle at \(3\) and the line should extend to the right, showing that all values greater than 3 satisfy the inequality.

Looking at the graphs in the image:
- The correct graph is **the second one on the right** (showing an open circle at 3 and the line pointing to the right).

Would you like more details or have any questions? 

Here are 5 related questions for practice:
1. How would the solution change if the inequality were \(2x + 5 \geq 11\)?
2. What happens if you change the inequality to \(2x + 5 < 11\)?
3. Can you explain the meaning of an open versus a closed circle on the graph?
4. How would you solve \(2x + 5 < -1\)?
5. How do you graph an inequality like \(x \geq -4\)?

**Tip:** Always remember to reverse the inequality sign if you multiply or divide by a negative number when solving inequalities!

Solve and graph the following inequality: 2x + 5 > 11.

Learn how to solve the inequality 2x + 5 > 11 with a step-by-step guide, including graphing the solution on a number line. This problem demonstrates essential concepts in algebra, including solving linear inequalities and graph interpretation. Ideal for students in Grades 6-8.

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