What is the solution of the inequality ∣2x+3∣≤7
 ?
A.[−5,2]

B.(−5,2)

C.[−2,5]

D.(−2,5)


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.** \( [-5, 2] \).

---

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!

What is the solution of the inequality ∣2x+3∣≤7?

Learn how to solve the absolute value inequality |2x+3| ≤ 7 step-by-step. This algebra problem breaks down the inequality into a compound inequality, solving it to find the interval [-5, 2]. Suitable for students in Grades 9-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation