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What does the set \{x | x > -14\} represent?\newlineChoices:\newline(A)all numbers less than 14-14 \newline(B)all numbers greater than or equal to 14-14 \newline(C)all numbers greater than 14-14 \newline(D)all numbers less than or equal to 14-14

Full solution

Q. What does the set {xx>14}\{x | x > -14\} represent?\newlineChoices:\newline(A)all numbers less than 14-14 \newline(B)all numbers greater than or equal to 14-14 \newline(C)all numbers greater than 14-14 \newline(D)all numbers less than or equal to 14-14
  1. Understand set notation: Understand the set notation. The set {x | x > -14} uses the inequality sign '>\', which means 'greater than'. We need to determine what range of numbers this set includes based on the inequality.
  2. Match to correct choice: Match the set notation to the correct choice. Since the inequality sign is '\(>', we are looking for numbers that are greater than 14-14, not less than or equal to 14-14, and not including 14-14 itself.
  3. Eliminate incorrect choices: Eliminate incorrect choices based on the inequality sign. \newline(A) Incorrect, because it says "less than 14-14" and we need "greater than 14-14".\newline(B) Incorrect, because it includes numbers equal to 14-14, and we need strictly greater than 14-14.\newline(D) Incorrect, because it says "less than or equal to 14-14" which is the opposite of what we need.
  4. Confirm correct choice: Confirm the correct choice. \newline(C) This choice says "all numbers greater than 14-14", which matches our set notation \{x | x > -14\}. Therefore, this is the correct choice.

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