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What does the set {xx15}\{x | x \geq -15\} represent?\newlineChoices:\newline(A)all numbers less than 15-15 \newline(B)all numbers greater than 15-15 \newline(C)all numbers greater than or equal to 15-15 \newline(D)all numbers equal to 15-15

Full solution

Q. What does the set {xx15}\{x | x \geq -15\} represent?\newlineChoices:\newline(A)all numbers less than 15-15 \newline(B)all numbers greater than 15-15 \newline(C)all numbers greater than or equal to 15-15 \newline(D)all numbers equal to 15-15
  1. Set Description: The set xx15{x | x \geq -15} is read as "the set of all xx such that xx is greater than or equal to 15-15." This is a description of a range of numbers on the number line.
  2. Inequality Consideration: To understand what this set represents, we need to consider the inequality x15x \geq -15. This inequality includes all numbers that are greater than 15-15 as well as the number 15-15 itself.
  3. Inequality Inclusion: The inequality does not only include numbers greater than 15-15, but also the number 15-15, as indicated by the 'greater than or equal to' symbol (\geq). Therefore, it cannot represent only numbers greater than 15-15 or only numbers equal to 15-15.
  4. Correct Representation: Given the choices provided, the correct representation of the set xx15{x | x \geq -15} is all numbers greater than or equal to 15-15, which corresponds to choice (C).

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