Understanding Absolute Value Equations

The video tutorial explains how to solve an absolute value equation involving nested absolute values. It begins by introducing the concept of absolute value equations and then demonstrates solving the outer and inner absolute values separately. The tutorial provides step-by-step solutions and concludes with a graphical verification using Desmos to confirm the solutions.

What is the basic form of an absolute value equation?

• Absolute value of x equals infinity

• Absolute value of x equals zero

• Absolute value of x equals a variable

• Absolute value of x equals a constant

When solving an absolute value equation, how many equations do you typically set up?

• Four

• Three

• Two

• One

What is the first step in solving the equation |4x - 1| - 9 = 2?

• Divide both sides by 9

• Add 9 to both sides

• Subtract 9 from both sides

• Multiply both sides by 9

What are the solutions for the equation 4x - 1 = 11?

• x = 5

• x = 2

• x = 4

• x = 3

What is the solution for the equation 4x - 1 = -7?

• x = -2

• x = -3

• x = -2.5

• x = -1.5

How many solutions are there for the given absolute value equation?

• Five

• Two

• Three

• Four

What tool is used to graphically verify the solutions?

• GraphCalc

• Desmos

• Wolfram Alpha

• GeoGebra

What does the intersection of the graphs represent?

• The y-values where the solutions are incorrect

• The y-values where the solutions are correct

• The x-values where the solutions are correct

• The x-values where the solutions are incorrect

Which color represents the graph of the left side of the equation?

• Turquoise

• Green

• Blue

• Pink

What is the y-value of the horizontal line in the graph?

• 1

• 2

• 4

• 3