To solve the inequality $|2x + 3| \leq 7$, we follow these steps:

Step 1: Break the absolute value inequality into two cases

An absolute value inequality of the form $|A| \leq B$ means: $-B \leq A \leq B$ So, for $|2x + 3| \leq 7$, we have: $-7 \leq 2x + 3 \leq 7$

Step 2: Solve the compound inequality

Now, solve this inequality step by step:

1. Subtract 3 from all parts: $-7 - 3 \leq 2x \leq 7 - 3$ $-10 \leq 2x \leq 4$

2. Divide all parts by 2: $\frac{-10}{2} \leq x \leq \frac{4}{2}$ $-5 \leq x \leq 2$

Step 3: Write the solution

The solution is the interval: $[-5, 2]$

Conclusion:

The correct answer is A. $[-5, 2]$.

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Would you like more details or have any questions?

Here are 5 related questions to consider:

1. How do you solve inequalities involving absolute values?
2. What is the difference between a closed interval $[a, b]$ and an open interval $(a, b)$?
3. How do you graph the solution to $|2x + 3| \leq 7$ on a number line?
4. How would the solution change if the inequality were $|2x + 3| < 7$?
5. Can you solve $|2x + 3| \geq 7$?

Tip: When solving absolute value inequalities, always remember to split the inequality into two cases—positive and negative—to cover all possible solutions!