Math Problem Statement

-|2x + 1| = -3

Solution

The equation provided is:

2x+1=3- |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 1-1 to simplify:

2x+1=3|2x + 1| = 3

Step 2: Apply the definition of absolute value

The absolute value equation can be broken into two cases:

  1. 2x+1=32x + 1 = 3
  2. 2x+1=32x + 1 = -3

Step 3: Solve each case

Case 1: 2x+1=32x + 1 = 3

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.

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Math Problem Analysis

Mathematical Concepts

Algebra
Absolute Value Equations

Formulas

|ax + b| = c
ax + b = c or ax + b = -c

Theorems

Absolute Value Theorem

Suitable Grade Level

Grades 7-9