Exploring Interval Notation and Linear Inequalities

This video tutorial introduces interval notation, a method for describing sections of the real number line. The instructor, Kirk Wier, explains how interval notation is used to represent inequalities and provides exercises to practice this concept. The lesson also covers the differences between interval notation and other forms of notation, such as inequality notation. The video concludes with a summary of the key points and the importance of understanding interval notation in algebra.

What is interval notation primarily used for?

• To solve quadratic equations

• To describe sections of the real number line

• To calculate derivatives

• To graph linear functions

Which of the following is the correct interval notation for the inequality -3 ≤ x ≤ 5?

• (-3, 5]

• (-3, 5)

• [3, 5]

• [-3, 5]

How do you represent an interval where -6 < x < 4 in interval notation?

• (-6, 4)

• [-6, 4)

• [-6, 4]

• (-6, 4]

In interval notation, what symbol is used to indicate that an endpoint is not included?

• Bracket [ ]

• Parenthesis ( )

• Curly brace { }

• Angle bracket < >

What is the interval notation for the inequality x > 4?

• [4, ∞]

• (4, ∞]

• (4, ∞)

• [4, ∞)

Which interval notation represents the inequality -4 < x ≤ 8?

• (-4, 8)

• [-4, 8)

• (-4, 8]

• [-4, 8]

What is the interval notation for the inequality x < 5?

• (-∞, 5]

• (-∞, 5)

• (-∞, 5)

• (-∞, 5]

How would you represent the solution set for the compound inequality -3 ≤ x < 2?

• [-3, 2]

• (-3, 2]

• [-3, 2)

• (-3, 2)

Which interval notation represents all values that are solutions to either of the inequalities -3 ≤ x < 2 or 0 < x < 4?

• (-3, 4]

• [-3, 4)

• [-3, 4]

• (-3, 4)

If pump one is on from 0 to 8 (excluding 8) and pump two is on from 4 to 18 (excluding 18), when are both pumps on?

• [4, 8]

• (4, 8]

• [4, 8)

• (4, 8)