What does the set \{x | x > -14\} represent?Choices:(A)all numbers less than −14(B)all numbers greater than or equal to −14(C)all numbers greater than −14(D)all numbers less than or equal to−14
Q. What does the set {x∣x>−14} represent?Choices:(A)all numbers less than −14(B)all numbers greater than or equal to −14(C)all numbers greater than −14(D)all numbers less than or equal to −14
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.
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, not less than or equal to −14, and not including −14 itself.
Eliminate incorrect choices: Eliminate incorrect choices based on the inequality sign. (A) Incorrect, because it says "less than −14" and we need "greater than −14".(B) Incorrect, because it includes numbers equal to −14, and we need strictly greater than −14.(D) Incorrect, because it says "less than or equal to −14" which is the opposite of what we need.
Confirm correct choice: Confirm the correct choice. (C) This choice says "all numbers greater than −14", which matches our set notation \{x | x > -14\}. Therefore, this is the correct choice.