Math Problem Statement
Solve the equation |2x - 4| = 13.
Solution
The equation provided is:
To solve absolute value equations like this, we need to consider two cases:
Case 1:
The expression inside the absolute value is positive or zero, so we can remove the absolute value bars:
Solve for :
2x = 17 \\ x = \frac{17}{2} \\ x = 8.5$$ ### Case 2: The expression inside the absolute value is negative, so we remove the absolute value bars and negate the right-hand side: $$2x - 4 = -13$$ Solve for $$x$$: $$2x = -13 + 4 \\ 2x = -9 \\ x = \frac{-9}{2} \\ x = -4.5$$ ### Final Answer: The solutions are $$x = 8.5$$ and $$x = -4.5$$. Would you like more details, or have any questions? Here are some related questions for further practice: 1. Solve $$|3x + 2| = 10$$. 2. Solve $$|x - 5| = 8$$. 3. What happens if $$|2x - 4| = -5$$? 4. Solve $$|4x + 1| = 7$$. 5. Solve $$|x| = 12$$. **Tip:** When solving absolute value equations, always remember to create two cases: one where the expression inside the absolute value is positive, and one where it's negative.Ask a new question for Free
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Math Problem Analysis
Mathematical Concepts
Absolute Value Equations
Linear Equations
Formulas
|A| = B implies A = B or A = -B
Theorems
Absolute Value Property
Suitable Grade Level
Grades 8-10