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!