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Advanced Math
/ Nonlinear equations in one variable and systems of equations in two variables
Difficulty: Medium
If , what is the positive value of ?
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Explanation
The correct answer is . The given absolute value equation can be rewritten as two linear equations: and , or . Adding to both sides of the equation results in . Dividing both sides of this equation by results in . Adding to both sides of the equation results in . Dividing both sides of this equation by results in . Therefore, the two values of are , or , and , or . Thus, the positive value of is .
Alternate approach: The given equation can be rewritten as , which is equivalent to . Dividing both sides of this equation by yields . This equation can be rewritten as two linear equations: and , or . Therefore, the positive value of is .