Question

Use the number line to express the following: all real numbers less than −2 or greater than or equal to 3.

a. (−[infinity],−2)∪[3,+[infinity])
b. (−[infinity],−2]∪[3,+[infinity])
c. (−[infinity],−2)∪(3,+[infinity])
d. (−[infinity],−2]∪(3,+[infinity])

Answer 1

The correct number line expression for all real numbers less than − 2 or greater than or equal to 3 is represented by (−∞,−2) ∪ [3,+∞), which is Option a.

Step-by-step explanation:

The question asks us to use a number line to express all real numbers less than − 2 or greater than or equal to 3. This is a compound inequality, and in mathematical notation, we use union (represented by ∪) to combine the two sets of numbers. Let's break down each option provided:

• Option a: (−∞,−2) ∪ [3,+∞) - This means all numbers less than -2 (not including -2 itself) and all numbers greater than or equal to 3.
• Option b: (−∞,−2] ∪ [3,+∞) - This means all numbers less than or equal to -2 and all numbers greater than or equal to 3.
• Option c: (−∞,−2) ∪ (3,+∞) - This means all numbers less than -2 and all numbers greater than 3 (not including 3).
• Option d: (−∞,−2] ∪ (3,+∞) - This means all numbers less than or equal to -2 and all numbers greater than 3 (not including 3).

Since we are looking for all real numbers less than −2 and greater than or equal to 3, the correct answer is the one that includes all numbers only up to −2 (not including −2 itself) and also includes the number 3 and all numbers greater. Therefore, the correct answer is Option a: (−∞,−2) ∪ [3,+∞).