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What interval does this inequality represent?\newline3 < x \leq 6\newlineChoices:\newline(A) [3,6][3, 6]\newline(B) [3,6)[3, 6)\newline(C) (3,6)(3, 6)\newline(D) (3,6](3, 6]

Full solution

Q. What interval does this inequality represent?\newline3<x63 < x \leq 6\newlineChoices:\newline(A) [3,6][3, 6]\newline(B) [3,6)[3, 6)\newline(C) (3,6)(3, 6)\newline(D) (3,6](3, 6]
  1. Identify Endpoints: Identify the endpoints of the interval for the inequality 3 < x \leq 6. The endpoints are 33 and 66.
  2. Check Inclusion: Check whether the endpoints are included or not. In the inequality 3 < x \leq 6, 33 is not included because the inequality is strict (3 < x), but 66 is included because the inequality is non-strict (x6x \leq 6).
  3. Determine Interval: Determine the interval that the inequality 3 < x \leq 6 represents. Since 33 is not included, we use a parenthesis. Since 66 is included, we use a bracket. The interval is therefore (3,6](3, 6].

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