题目
题目
单项选择题

Consider the inequalities:[math: d1:(x−1)(x+3)≥0] d_1: \quad (x-1)(x+3) \ge 0 [math: d2:x−1x+3≥0] d_2: \quad \frac{x-1}{x+3} \ge 0

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The question presents an analysis of two inequalities: d1 is (x−1)(x+3) ≥ 0, and d2 is (x−1)/(x+3) ≥ 0. First, determine the solution set for d1. The roots are at x = −3 and x = 1, and since the leading term of the product is positive, the product is ......Login to view full explanation

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Question textThe students below solved rational inequalities. Match each student’s reasoning to the best explanation.Student 1:“I solved \frac{1}{x+1} < 5 and wrote the solution intervals as x < -1 or x > -\frac{4}{5} .” Answer 1 Question 22[select: , The student found the correct critical points but only x < -1 is a valid interval; x > -4/5 is not valid., The student listed the correct critical points but mistakenly concluded the interval solution; the correct solution is -1 < x < -4/5., The student correctly solved the inequality and gave appropriate solution intervals using the correct critical points.]Student 2:“I solved \frac{2x}{x-1} > 3 and wrote x > 3 as my solution interval.” Answer 2 Question 22[select: , The student correctly identified the critical points and the solution; the correct interval is x > 3., The student identified the correct critical points, but the solution is incorrect; the correct solution is x < 1, x > 3., The student identified the correct critical points but the solution is incorrect; the correct solution is 1 < x < 3. ]Student 3:“I solved \frac{x+4}{x-3} < 2 and listed critical points at x = -4 and x = 3 .” Answer 3 Question 22[select: , The student correctly listed the critical values as x = -4 and x = 3., The student attempted to identify critical points but incorrectly listed x = -4; the correct critical points are x = 3 and x = 10., The student attempted to identify critical points but incorrectly listed x = -4 instead of x = 2; the correct critical points are x = 3 and x = 2.]

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Which of the following intervals are part of the solution set of  x 2 − 3 x − 4 x 2 − x − 2 ≥ 0 ? {"version":"1.1","math":"\dfrac{x^2-3x-4}{x^2-x-2}\ge 0?"}

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