Solve the absolute value equation . The solutions are and .
Answer & Analysis
Analysis
Question Analysis
This question tests the student's ability to solve an absolute value equation by isolating the absolute value expression and then setting up two separate equations for the positive and negative cases.
Key Concept Explanation
The key concept is that the absolute value of a number is its distance from zero on the number line, always non-negative. To solve an absolute value equation, we isolate the absolute value expression and set up two separate equations: one with the positive value and one with the negative value.
Step-by-step Solution
1. Isolate the absolute value expression: Subtract 3 from both sides to get
2. Set up two equations: and
3. Solve each equation:
For : Add 1 to both sides to get
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