Question

Write the inequality using interval notation and illustrate the inequality using a real number line for the inequality X > 2.

a) (2, [infinity]) on the number line
b) [2, [infinity]) on the number line
c) (-[infinity], 2) on the number line
d) (-[infinity], 2] on the number line

Answer 1

To write the inequality X > 2 using interval notation, the correct answer is (2, ∞) on the number line. To illustrate this inequality on a real number line, mark a point for 2, but do not include it, and shade the region to the right to show all values greater than 2.

Step-by-step explanation:

To write the inequality X > 2 using interval notation, we represent the set of all real numbers greater than 2. Interval notation uses parentheses for excluding the endpoints and brackets for including the endpoints. The correct answer is (2, ∞) on the number line.

To illustrate this inequality on a real number line, we start by marking a point on the number line for the value 2. Since the inequality is X > 2, the point representing 2 is not included. Then, we shade the region to the right of the point 2 to indicate all the values greater than 2.