Understanding Inequalities and Interval Notation

The video tutorial explains how to graph inequalities and express them using interval notation. It covers various inequalities, including simple and compound ones, and demonstrates how to represent them on a number line with open or closed points. The tutorial also explains the use of parentheses and brackets in interval notation, depending on whether endpoints are included in the interval.

What type of point is used to graph the inequality X < 5?

• Solid line

• Open point

• Closed point

• Square bracket

In interval notation, how is the inequality X < 5 expressed?

• (-∞, 5]

• (-∞, 5)

• [5, ∞)

• (5, ∞)

For the inequality X > -2, which direction do we graph?

• To the left

• Downwards

• To the right

• Upwards

How is the inequality X > -2 represented in interval notation?

• (-2, ∞)

• [-2, ∞)

• (-∞, -2]

• (-∞, -2)

What type of point is used to graph the inequality X ≤ -1?

• Arrow

• Dashed line

• Closed point

• Open point

How is the interval for X = 3 expressed in interval notation?

• (3, ∞)

• [3, ∞)

• [3, 3]

• (3, 3)

What is the interval notation for the inequality X ≥ 2?

• [2, ∞)

• (-∞, 2)

• (-∞, 2]

• (2, ∞)

In the compound inequality -3 ≤ X < 4, which numbers are included in the interval?

• -3 and 4

• -3 only

• Neither -3 nor 4

• 4 only

How is the compound inequality -3 ≤ X < 4 expressed in interval notation?

• (-3, 4]

• [-3, 4)

• [3, 4]

• (-3, 4)

For the compound inequality 8 < X ≤ 0, which endpoint is included in the interval?

• 8

• 0

• Both 8 and 0

• Neither 8 nor 0