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The equation provided is:

\[
- |2x + 1| = -3
\]

To solve this, follow these steps:

### Step 1: Remove the negative sign from both sides
Since both sides of the equation are negative, we can divide both sides by \(-1\) to simplify:

\[
|2x + 1| = 3
\]

### Step 2: Apply the definition of absolute value
The absolute value equation can be broken into two cases:

1. \(2x + 1 = 3\)
2. \(2x + 1 = -3\)

### Step 3: Solve each case

#### Case 1: \(2x + 1 = 3\)
\[
2x = 3 - 1 \\
2x = 2 \\
x = 1
\]

#### Case 2: \(2x + 1 = -3\)
\[
2x = -3 - 1 \\
2x = -4 \\
x = -2
\]

### Final Answer
The solutions are:

\[
x = 1 \quad \text{or} \quad x = -2
\]

Would you like further details or have any questions?

Here are 5 related questions you might find helpful:
1. How do you handle equations with multiple absolute values?
2. Can there be a case where no solution exists for absolute value equations?
3. How does adding or subtracting from both sides affect absolute value equations?
4. Can you solve more complex absolute value equations involving quadratics?
5. What happens if there's a coefficient outside the absolute value?

**Tip:** Always check whether simplifying both sides, like removing negatives, can make the equation easier to solve.

Learn how to solve the absolute value equation -|2x + 1| = -3 with detailed steps. This problem covers algebraic concepts like absolute value and provides a clear step-by-step solution. Suitable for students in Grades 7-9.

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