The problem asks to solve the inequality $|2x + 5| < 11$ and graph the solutions.

Step 1: Solve the inequality

The absolute value inequality $|2x + 5| < 11$ can be written as two separate inequalities:

1. $2x + 5 < 11$
2. $2x + 5 > -11$

Step 2: Solve both inequalities

• For $2x + 5 < 11$: $2x < 6 \quad \text{(subtract 5 from both sides)}$ $x < 3 \quad \text{(divide both sides by 2)}$

• For $2x + 5 > -11$: $2x > -16 \quad \text{(subtract 5 from both sides)}$ $x > -8 \quad \text{(divide both sides by 2)}$

Step 3: Combine the results

The solution to the inequality is the combination of both: $-8 < x < 3$

Step 4: Graph the solution

The solution $-8 < x < 3$ is shown as a line segment on the number line, excluding the points $-8$ and $3$.

Step 5: Select the correct graph

The correct graph will show the open interval between $-8$ and $3$, which corresponds to the first option:
$-8 < x < 3$.

Would you like more details on this process or any further clarifications? Here are some related questions you may find helpful:

1. What is the difference between an open and closed interval on a number line?
2. How do you solve inequalities involving absolute value?
3. What is the meaning of "and" vs. "or" in compound inequalities?
4. How would the solution change if the inequality were $|2x + 5| \leq 11$?
5. Can you graph inequalities with absolute values that involve "greater than" instead of "less than"?

Tip: Always break absolute value inequalities into two cases—one for the positive expression and one for the negative—then solve each part separately.