Exploring Absolute Value Equations and Inequalities

The video tutorial covers solving absolute value equations and inequalities. It begins with an introduction to absolute value, explaining its definition and significance. The instructor demonstrates how to solve absolute value equations by isolating the absolute value, setting up two equations, and solving them. The process of checking solutions is also explained. Additional examples are provided, including cases where no solution exists. The tutorial compares linear equations with absolute value equations and concludes with solving absolute value inequalities, highlighting the importance of flipping the inequality sign when dividing by a negative.

What does the absolute value of a number represent?

• The square of the number

• The distance from zero

• The negative of the number

• The number itself

If the absolute value of x is 3, what are the possible values of x?

• 3 and -3

• 3 and 0

• 3 and 6

• 3 and -6

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

• Multiply both sides by a constant

• Isolate the absolute value expression

• Add a constant to both sides

• Subtract a constant from both sides

How do you check the solutions of an absolute value equation?

• By graphing the equation

• By solving a different equation

• By using a calculator

• By substituting the solutions back into the original equation

What happens to the inequality sign when you divide by a negative number?

• It becomes an equal sign

• It flips

• It stays the same

• It disappears

In the inequality |x - 2| > 5, what are the two resulting inequalities?

• x - 2 > 5 and x - 2 < 5

• x - 2 > 5 and x - 2 < -5

• x - 2 < 5 and x - 2 < -5

• x - 2 > 5 and x - 2 > -5

What is the solution to the inequality |2x + 3| < 7?

• -4 < x < 2

• -5 < x < 1

• -2 < x < 2

• -5 < x < 2

If the absolute value of x + 2 equals -2, what is the solution?

• x = 2

• x = 0

• x = -4

• No solution

What is the solution to the equation |2x + 3| = 11?

• x = 5 or x = -7

• x = 5 or x = -8

• x = 4 or x = -8

• x = 4 or x = -7

How can you verify your solution to an absolute value inequality?

• By substituting the solution back into the inequality

• By solving a different inequality

• By graphing the inequality

• By using a calculator