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Which is the set of numbers greater than −3-3 and less than 44?\newlineChoices:\newline(A){x∣x≥−3 and x≤4}\{x | x \geq -3 \text{ and } x \leq 4\} \newline(B)\{x | x < -3 \text{ and } x > 4\} \newline(C)\{x | x > -3 \text{ and } x < 4\} \newline(D){x∣x≤−3 and x≥4}\{x | x \leq -3 \text{ and } x \geq 4\}

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Q. Which is the set of numbers greater than −3-3 and less than 44?\newlineChoices:\newline(A){x∣x≥−3 and x≤4}\{x | x \geq -3 \text{ and } x \leq 4\} \newline(B){x∣x<−3 and x>4}\{x | x < -3 \text{ and } x > 4\} \newline(C){x∣x>−3 and x<4}\{x | x > -3 \text{ and } x < 4\} \newline(D){x∣x≤−3 and x≥4}\{x | x \leq -3 \text{ and } x \geq 4\}
  1. Understand the problem: Understand the problem. We need to find the set of numbers that are greater than −3-3 and also less than 44.
  2. Identify inequality signs: Identify the correct inequality signs for the conditions given. For numbers greater than −3-3, we use the > sign. For numbers less than 44, we use the < sign.
  3. Combine conditions in set notation: Combine the two conditions with the correct inequality signs to form the set notation. The set notation should include both conditions: numbers greater than −3-3 and numbers less than 44.
  4. Review choices: Review the choices given and match them with our set notation from Step 33. We are looking for a choice that correctly represents both conditions: x > -3 and x < 4.
  5. Choice (A) analysis: Choice (A) x∣x≥−3 and x≤4{x | x \geq -3 \text{ and } x \leq 4} includes numbers that are equal to −3-3 and 44, which is not what we want because we need numbers strictly greater than −3-3 and strictly less than 44.
  6. Choice (B) analysis: Choice (B) {x | x < -3 \text{ and } x > 4} represents numbers that are less than −3-3 and greater than 44, which is the opposite of what we are looking for.
  7. Choice (C) analysis: Choice (C) {x | x > -3 \text{ and } x < 4} correctly represents the set of numbers that are greater than −3-3 and less than 44. This matches our set notation from Step 33.
  8. Choice (D) analysis: Choice (D) x∣x≤−3 and x≥4{x | x \leq -3 \text{ and } x \geq 4} includes numbers that are equal to −3-3 and 44, and also represents the set of numbers that are less than or equal to −3-3 and greater than or equal to 44, which is not the correct set.

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