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What does the set \{x | x > -6 \text{ and } x < -3\} represent?\newlineChoices:\newline(A)all numbers greater than or equal to 6-6 and less than or equal to 3-3 \newline(B)all numbers greater than 6-6 and less than or equal to 3-3 \newline(C)all numbers less than or equal to 6-6 and greater than or equal to 3-3 \newline(D)all numbers greater than 6-6 and less than 3-3

Full solution

Q. What does the set {xx>6 and x<3}\{x | x > -6 \text{ and } x < -3\} represent?\newlineChoices:\newline(A)all numbers greater than or equal to 6-6 and less than or equal to 3-3 \newline(B)all numbers greater than 6-6 and less than or equal to 3-3 \newline(C)all numbers less than or equal to 6-6 and greater than or equal to 3-3 \newline(D)all numbers greater than 6-6 and less than 3-3
  1. Understand set notation: Understand the set notation. The set {x | x > -6 \text{ and } x < -3} describes all the numbers xx that satisfy two conditions: xx must be greater than 6-6 and xx must be less than 3-3.
  2. Determine interval notation: Determine the correct interval notation. Since the conditions are x > -6 and x < -3, we are looking for numbers that are strictly greater than 6-6 and strictly less than 3-3. This means that 6-6 and 3-3 are not included in the set.
  3. Match interval choices: Match the interval to the given choices. The interval described by the set notation is an open interval, which means neither endpoint is included. Therefore, we can eliminate choices (A)(A) and (C)(C) because they include the endpoints with “greater than or equal to”\text{“greater than or equal to”} and “less than or equal to”\text{“less than or equal to”}.
  4. Compare remaining choices: Compare the remaining choices. Choice (B) includes 3-3 with \leq, which is not correct because our set does not include 3-3. Choice (D) correctly states greater than 6 and less than 3\text{greater than } -6 \text{ and less than } -3, which matches our set notation.

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