Understanding Absolute Value Equations and Inequalities

This video tutorial introduces the concept of absolute value, explaining it as the distance of a number from zero, which is always non-negative. It covers solving absolute value equations, demonstrating that such equations can have two solutions or none, depending on the values involved. The tutorial also explores absolute value inequalities, showing how to determine solution sets and graph them on a number line, using both open and closed intervals. The video emphasizes understanding the graphical representation and interval notation for these mathematical concepts.

What is the absolute value of a number?

• The number's distance from zero

• The number itself

• The negative of the number

• The number's distance from one

If the absolute value of x is 2, what are the possible values of x?

• Only 2

• Only -2

• 0 and 2

• 2 and -2

Which of the following is true for the absolute value equation |x| = 3?

• x can be 3 or -3

• x can only be -3

• x can only be 3

• x can be any number

What does the inequality |x| < 2 represent?

• x is not equal to 2

• x is between -2 and 2

• x is less than 2

• x is greater than 2

In the inequality |x| ≤ 2, which numbers are included in the solution set?

• Only numbers between -2 and 2, excluding -2 and 2

• Only numbers greater than 2

• Numbers between -2 and 2, including -2 and 2

• Only numbers less than -2

What does the interval notation (-2, 2) represent?

• All numbers greater than 2

• Only the numbers -2 and 2

• All numbers between -2 and 2, excluding -2 and 2

• All numbers between -2 and 2, including -2 and 2

What is the significance of using a square bracket in interval notation?

• It indicates that the endpoint is not included

• It indicates that the endpoint is included

• It indicates an infinite interval

• It indicates a negative interval

How is the solution set for |x| > 2 represented on a number line?

• A line extending from -2 to the left and from 2 to the right

• A point at 2

• A point at -2

• A line between -2 and 2

Which of the following is a correct representation of the solution set for |x| ≥ 2?

• (2, ∞)

• (-∞, -2) ∪ (2, ∞)

• (-2, 2)

• (-∞, 2)

How can the solution set for |x| > 2 be expressed using interval notation?

• (-2, 2)

• (-∞, -2) ∪ (2, ∞)

• [2, ∞)

• (-∞, 2]