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What does the set {xx5 and x3}\{x | x \geq -5 \text{ and } x \leq 3\} represent?\newlineChoices:\newline(A)all numbers greater than or equal to 5-5 and less than 33 \newline(B)all numbers greater than or equal to 5-5 and less than or equal to 33 \newline(C)all numbers less than 5-5 and greater than 33 \newline(D)all numbers less than 5-5 and greater than 33

Full solution

Q. What does the set {xx5 and x3}\{x | x \geq -5 \text{ and } x \leq 3\} represent?\newlineChoices:\newline(A)all numbers greater than or equal to 5-5 and less than 33 \newline(B)all numbers greater than or equal to 5-5 and less than or equal to 33 \newline(C)all numbers less than 5-5 and greater than 33 \newline(D)all numbers less than 5-5 and greater than 33
  1. Understand set notation: Understand the set notation. The set xx5 and x3{x | x \geq -5 \text{ and } x \leq 3} includes all numbers xx that satisfy two conditions: xx is greater than or equal to 5-5, and xx is less than or equal to 33.
  2. Identify correct interval: Identify the correct interval. The notation x5x \geq -5 means all numbers that are 5-5 or higher, and x3x \leq 3 means all numbers that are 33 or lower. The set includes all numbers that are both greater than or equal to 5-5 and less than or equal to 33 at the same time.
  3. Match with correct choice: Match the set with the correct choice. The set represents an interval on the number line from 5-5 to 33, including both endpoints. This corresponds to all numbers greater than or equal to 5-5 and less than or equal to 33.

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