Absolute Value Equations and Intervals

The video tutorial explains how to solve an absolute value equation involving two expressions. It begins by determining the zeros of each expression, then divides the number line into intervals based on these zeros. The tutorial evaluates the inputs over these intervals, replacing absolute values with appropriate expressions. It then solves the resulting equations, checking if solutions fall within the specified intervals. Finally, the solutions are verified graphically by plotting the equations and identifying points of intersection.

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

• Isolate the absolute values and find their zeros

• Add a constant to both sides

• Multiply both sides by a constant

• Graph the equation

How is the number line divided after determining the zeros of the absolute values?

• Into five intervals

• Into four intervals

• Into two intervals

• Into three intervals

What do you do if the input of an absolute value is negative over an interval?

• List the original input

• List the opposite input

• Ignore the input

• Double the input

In the interval from -2/3 to 12, which expression remains positive?

• Both expressions

• Neither expression

• 3x + 2

• 2x - 1

What is the equation set up for the interval from 1/2 to Infinity?

• -2x + 1 + 3x + 2 = 4

• 2x - 1 + 3x + 2 = 4

• -2x + 1 - 3x - 2 = 4

• 2x - 1 - 3x - 2 = 4

What is the solution for the equation in the interval from negative Infinity to -2/3?

• x = 2

• x = 0

• x = -1

• x = 1

Why is x = 1 not a solution in the interval from -2/3 to 12?

• It is less than 1/2

• It is greater than 1/2

• It is greater than 12

• It is less than -2/3

What is the solution for the equation in the interval from 1/2 to Infinity?

• x = 1

• x = 0.6

• x = 2

• x = -1

How can the solutions be verified graphically?

• By checking the slope of the graph

• By finding the points of intersection

• By calculating the area under the curve

• By determining the y-intercept

What are the final solutions to the original absolute value equation?

• x = -1 and x = 0.6

• x = 1 and x = 0.6

• x = 0 and x = 1

• x = -1 and x = 1