The solutions to the inequality (2-x)(x+1)x 2 B: 0

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The solutions to the inequality (2-x)(x+1)x < 0 are: A: x > 2 B: 0 < x < 1 or x > 2 C: x < -1 or 0 < x < 2 D: -1 < x < 0 or x > 2 E: -1 < x < 0

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Identify critical points: Identify the critical points of the inequality by setting each factor to zero. (2-x)(x+1)x < 0 Set each factor to zero: 2 - x = 0 => x = 2 x + 1 = 0 => x = -1 x = 0 The critical points are x = -1, x = 0, and x = 2.Determine intervals: Determine the intervals to test around the critical points. The intervals are: (-∞, -1), (-1, 0), (0, 2), and (2, ∞).Test each interval: Test each interval to see if the inequality holds true. Choose a test point from each interval and plug it into the inequality. For (-∞, -1), let's choose x = -2: (2 - (-2))((-2) + 1)(-2) = (4)(-1)(-2) = 8 > 0, so this interval does not satisfy the inequality.Test (-∞, -1): Test the interval (-1, 0). Choose x = -0.5: (2 - (-0.5))((-0.5) + 1)(-0.5) = (2.5)(0.5)(-0.5) = -0.625 < 0, so this interval satisfies the inequality.Test (-1, 0): Test the interval (0, 2). Choose x = 1: (2 - 1)(1 + 1)(1) = (1)(2)(1) = 2 > 0, so this interval does not satisfy the inequality.Test (0, 2): Test the interval (2, ∞). Choose x = 3: (2 - 3)(3 + 1)(3) = (-1)(4)(3) = -12 < 0, so this interval satisfies the inequality.Test (2, ∞): Combine the intervals that satisfy the inequality. From our tests, the intervals that satisfy the inequality are: -1 < x < 0 and x > 2.Combine intervals: Match the combined intervals with the given choices. The correct answer is D: -1 < x < 0 or x > 2.

The solutions to the inequality $\newline$ (2-x)(x+1)x < 0 are: $\newline$ A: $\newline$ x > 2 $\newline$ B: $\newline$ 0 < x < 1 or $\newline$ x > 2 $\newline$ C: $\newline$ x < -1 or $\newline$ 0 < x < 2 $\newline$ D: $\newline$ -1 < x < 0 or $\newline$ x > 2 $\newline$ E: $\newline$ -1 < x < 0

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The solutions to the inequality \newline(2-x)(x+1)x < 0 are:\newlineA: \newlinex > 2\newlineB: \newline0 < x < 1 or \newlinex > 2\newlineC: \newlinex < -1 or \newline0 < x < 2\newlineD: \newline-1 < x < 0 or \newlinex > 2\newlineE: \newline-1 < x < 0

The solutions to the inequality $\newline$ (2-x)(x+1)x < 0 are: $\newline$ A: $\newline$ x > 2 $\newline$ B: $\newline$ 0 < x < 1 or $\newline$ x > 2 $\newline$ C: $\newline$ x < -1 or $\newline$ 0 < x < 2 $\newline$ D: $\newline$ -1 < x < 0 or $\newline$ x > 2 $\newline$ E: $\newline$ -1 < x < 0