https://file.aiquickdraw.com/mathbot/file/1727355556314xy5e5x5t.jpg

The image contains the inequality:

\[
-4 \leq 3x + 2 < 5
\]

To solve this inequality, we need to break it down into two parts:

1. \(-4 \leq 3x + 2\)
2. \(3x + 2 < 5\)

### Step 1: Solve \(-4 \leq 3x + 2\)
Subtract 2 from both sides:
\[
-4 - 2 \leq 3x
\]
\[
-6 \leq 3x
\]
Now, divide both sides by 3:
\[
-2 \leq x
\]
Thus, \(x \geq -2\).

### Step 2: Solve \(3x + 2 < 5\)
Subtract 2 from both sides:
\[
3x < 5 - 2
\]
\[
3x < 3
\]
Now, divide both sides by 3:
\[
x < 1
\]

### Final Solution:
The solution to the inequality is:
\[
-2 \leq x < 1
\]
In interval notation, this is:
\[
x \in [-2, 1)
\]

Let me know if you'd like more details on any step! 

Here are some related questions:
1. How do you graph compound inequalities on a number line?
2. How do you solve inequalities that involve multiplying or dividing by negative numbers?
3. What is the difference between open and closed intervals in inequalities?
4. How do you check if a solution satisfies the original inequality?
5. Can compound inequalities be solved using absolute values?

**Tip**: Always pay attention to the inequality signs. They determine if the endpoints are included or excluded.

Learn how to solve the compound inequality -4 ≤ 3x + 2 < 5 using step-by-step algebraic methods. This problem is suitable for students in Grades 7-9 and covers core concepts in inequalities.

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