Math Problem Statement
-|2x + 1| = -3
Solution
The equation provided is:
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 to simplify:
Step 2: Apply the definition of absolute value
The absolute value equation can be broken into two cases:
Step 3: Solve each case
Case 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.Ask a new question for Free
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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