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What inequality represents this interval?\newline(−3,2)(-3, 2)\newlineChoices:\newline(A) −3≤x≤2-3 \leq x \leq 2\newline(B) -3 < x \leq 2\newline(C) -3 \leq x < 2\newline(D) -3 < x < 2

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Full solution

Q. What inequality represents this interval?\newline(−3,2)(-3, 2)\newlineChoices:\newline(A) −3≤x≤2-3 \leq x \leq 2\newline(B) −3<x≤2-3 < x \leq 2\newline(C) −3≤x<2-3 \leq x < 2\newline(D) −3<x<2-3 < x < 2
  1. Identify Endpoints: Identify the endpoints of the interval and whether they are included in the interval. The interval (−3,2) (-3, 2) has endpoints at −3 -3 and 2 2 , and since they are in parentheses, neither endpoint is included in the interval.
  2. Translate to Inequality: Translate the interval into an inequality. Since neither −3-3 nor 22 is included, the inequality must use strict inequality signs. The inequality that represents all numbers greater than −3-3 and less than 22 is -3 < x < 2.
  3. Match with Choices: Match the inequality with the given choices. The inequality -3 < x < 2 corresponds to choice (D).

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