Understanding Absolute Value Inequalities

The video tutorial explains how to solve absolute value inequalities by expressing solutions as compound inequalities, graphs, and using interval notation. It covers two basic examples: absolute value of x < 4 and x > 4, demonstrating how to graph these inequalities and express them in different forms. The tutorial also discusses the use of intersection and union symbols in compound inequalities and provides detailed examples to illustrate these concepts.

What is the primary goal when solving absolute value inequalities?

• To determine if x is positive or negative

• To express the solution as a compound inequality, graph, and interval notation

• To simplify the inequality to a single equation

• To find the exact value of x

For the inequality |x| < 4, which of the following represents the correct compound inequality?

• x > 4 or x < -4

• x < 4 and x > -4

• x > 4 and x < -4

• x < 4 or x > -4

In the graph of |x| < 4, what does the shaded region represent?

• All negative numbers

• All positive numbers

• Numbers with a distance from 0 less than 4

• Numbers with a distance from 0 greater than 4

For the inequality |x| > 4, which of the following represents the correct compound inequality?

• x > 4 or x < -4

• x > 4 and x < -4

• x < 4 and x > -4

• x < 4 or x > -4

In the graph of |x| > 4, what does the shaded region represent?

• Numbers with a distance from 0 less than 4

• Numbers with a distance from 0 greater than 4

• All numbers between -4 and 4

• All numbers greater than 0

How is the solution of |x| < 4 expressed in interval notation?

• [-4, 4]

• (-∞, -4) ∪ (4, ∞)

• [4, ∞)

• (-4, 4)

How is the solution of |x| > 4 expressed in interval notation?

• (-∞, 4)

• [4, ∞)

• (-∞, -4) ∪ (4, ∞)

• (-4, 4)

What does the intersection symbol (∩) represent in compound inequalities?

• The complement of a set

• The union of two sets

• The difference between two sets

• The intersection of two sets

What does the union symbol (U) represent in compound inequalities?

• The difference between two sets

• The union of two sets

• The complement of a set

• The intersection of two sets

Which of the following is true about the use of 'and' and 'or' in compound inequalities?

• 'And' is used for intersection, 'or' is used for union

• 'And' is used for union, 'or' is used for intersection

• Both 'and' and 'or' are used for union

• Both 'and' and 'or' are used for intersection