Exploring Order and Interval Notation

This video tutorial by Mr. Back Work covers the order of real numbers and the use of interval notation. It explains how real numbers are ordered and how inequalities can be used to compare them. The tutorial includes graphing inequalities on a number line, interpreting intervals, and converting verbal descriptions into inequalities. It also discusses bounded and unbounded intervals, and how to write them in interval notation. The video concludes with examples of converting between interval notation and inequalities.

What does it mean when a number is further to the right on a number line?

• It is a smaller value.

• It is a larger value.

• It is a negative value.

• It is an undefined value.

Which inequality correctly represents that 3 is greater than -2?

• 3 < -2

• -2 > 3

• 3 = -2

• 3 > -2

How do you graph an inequality where the end value is not included?

• Using a dot

• Using a curly brace

• Using a parenthesis

• Using a square bracket

What does the inequality X < 3 represent on a number line?

• All numbers greater than 3

• All numbers equal to 3

• All numbers less than 3

• Only the number 3

In the inequality -1 < X ≤ 4, which value is included in the interval?

• Neither -1 nor 4

• Both -1 and 4

• 4

• -1

How do you represent an interval where the end values are included?

• Using parentheses

• Using square brackets

• Using curly braces

• Using dots

What is the interval notation for X > 0?

• (0, ∞)

• [0, ∞)

• (0, ∞]

• [0, ∞]

How is the interval -∞ < X < B represented in interval notation?

• [-∞, B]

• (-∞, B)

• (-∞, B]

• [-∞, B)

Convert the interval [-6, 3) to an inequality.

• -6 < X < 3

• -6 ≤ X < 3

• -6 ≤ X ≤ 3

• -6 < X ≤ 3

What is the interval notation for the inequality -2 ≤ X ≤ 3?

• [-2, 3]

• [-2, 3)

• (-2, 3)

• (-2, 3]