Solving Absolute Value Inequalities

The video tutorial covers solving absolute value equations, absolute value inequalities, and quadratic inequalities. It begins with an overview of the topics, followed by detailed explanations and examples for each type of equation and inequality. The tutorial emphasizes the importance of isolating the absolute value, checking for extraneous roots, and using number lines for inequalities. Quadratic inequalities are introduced with a focus on factoring and setting one side equal to zero.

What topics are covered in this review session?

• Only absolute value inequalities

• Absolute value equations, inequalities, and quadratic inequalities

• Only quadratic inequalities

• Only absolute value equations

What is a key difference between solving absolute value equations and inequalities?

• Inequalities do not require any checks

• Equations require a number line

• Inequalities require a number line

• Equations require checking for extraneous roots

What is the first step in solving an absolute value equation?

• Check for extraneous roots

• Isolate the absolute value

• Use a number line

• Solve two equations

In the example problem, what was the solution for the absolute value equation?

• x = -3

• x = 3

• x = 9

• x = 0

What is necessary when solving absolute value inequalities?

• Using a number line to state the solution

• Checking for extraneous roots

• Solving only one equation

• Ignoring the inequality sign

In the example of an absolute value inequality, what was the solution range?

• x < -10

• x > 4

• All real numbers

• x = 0

What characterizes a quadratic inequality?

• It is solved without a number line

• It includes a squared term

• It has a linear term

• It requires no factoring

In the quadratic inequality example, what was the solution range?

• x = 0

• x = -5

• x > -5 and x < 0

• x < -5 or x > 0

How can solutions for inequalities be expressed?

• Only in set builder notation

• Only in interval notation

• In both set builder and interval notation

• In neither set builder nor interval notation