Math  /  Algebra

QuestionSolve. x+4x2<1\frac{x+4}{x-2}<1
The solution set is \square (Type your answer in interval notation.)

Studdy Solution
Test intervals defined by the critical point x=2x = 2 to determine where the inequality holds:
1. Interval: (,2)(-\infty, 2) - Choose a test point, e.g., x=0x = 0: 602=62=3<0 \frac{6}{0-2} = \frac{6}{-2} = -3 < 0 - The inequality holds.
2. Interval: (2,)(2, \infty) - Choose a test point, e.g., x=3x = 3: 632=61=6>0 \frac{6}{3-2} = \frac{6}{1} = 6 > 0 - The inequality does not hold.
The solution set is the interval where the inequality holds:
(,2) (-\infty, 2)
The solution set is:
(,2) \boxed{(-\infty, 2)}

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