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Which is the set of numbers less than 12-12 or greater than 33?\newlineChoices:\newline(A)\{x | x > -12 \text{ or } x < -3\} \newline(B){xx12 or x3}\{x | x \leq -12 \text{ or } x \geq -3\} \newline(C){xx12 or x3}\{x | x \geq -12 \text{ or } x \leq -3\} \newline(D)\{x | x < -12 \text{ or } x > 3\}

Full solution

Q. Which is the set of numbers less than 12-12 or greater than 33?\newlineChoices:\newline(A){xx>12 or x<3}\{x | x > -12 \text{ or } x < -3\} \newline(B){xx12 or x3}\{x | x \leq -12 \text{ or } x \geq -3\} \newline(C){xx12 or x3}\{x | x \geq -12 \text{ or } x \leq -3\} \newline(D){xx<12 or x>3}\{x | x < -12 \text{ or } x > 3\}
  1. Understand the problem: Understand the problem. We need to find the set of numbers that are either less than 12-12 or greater than 33.
  2. Identify inequality signs: Identify the correct inequality signs for the conditions given. For numbers less than 12-12, we use the "<" sign. For numbers greater than 33, we use the ">" sign.
  3. Translate into set notation: Translate the conditions into set notation. The set of numbers less than 12-12 is written as \{x | x < -12\}. The set of numbers greater than 33 is written as \{x | x > 3\}.
  4. Combine conditions: Combine the two conditions using the word "or" since we are looking for numbers that satisfy either condition. The correct set notation is {x | x < -12 \text{ or } x > 3}.
  5. Match with choices: Match our set notation with the given choices. The correct choice is (D)\{x | x < -12 \text{ or } x > 3\}.

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