Question

All real numbers that are less than -3 or greater than or equal to 5

a) x < -3x<−3 or x \geq 5x≥5
b) x \leq -3x≤−3 or x > 5x>5
c) x < -3x<−3 and x \geq 5x≥5
d) x \leq -3x≤−3 and x > 5x>5

Answer 1

The correct representation for all real numbers that are less than -3 or greater than or equal to 5 is b) x ≤ -3 or x > 5.

Step-by-step explanation:

To express the set of real numbers that are less than -3 or greater than or equal to 5, we use the combination of inequalities. The correct representation is given by x ≤ -3 (all real numbers less than or equal to -3) combined with x > 5 (all real numbers greater than 5). This ensures that we include the values less than -3 and the values greater than 5 in the solution set.

The option x ≤ -3 or x > 5 accurately captures this combination of inequalities. It correctly indicates that x can be any real number less than or equal to -3 or any real number greater than 5. This choice is the most suitable representation for the given condition, making option b) the correct answer.

In conclusion, the expression x ≤ -3 or x > 5 effectively represents the set of real numbers that are either less than -3 or greater than or equal to 5. The combination of these inequalities appropriately captures the range of values specified in the question.