Understanding Absolute Value Inequalities

This video tutorial explains how to write an absolute value inequality from a graph. It begins by identifying the 'home base' or midpoint between two boundary values. The distance between these values is calculated, and the midpoint is determined by halving this distance. The tutorial then shows how to incorporate the home base and distance into an absolute value inequality, using subtraction to express distance. The correct inequality symbol is chosen based on whether the situation requires staying close to home. The video concludes with a summary and encourages viewers to practice the concepts learned.

What is the main topic of the video?

• How to solve quadratic equations

• How to write an absolute value inequality from a graph

• How to find the slope of a line

• How to graph linear equations

What is the 'home base' in the context of the video?

• The starting point of a graph

• The midpoint between two boundary values

• The highest point on a graph

• The lowest point on a graph

What is the first step in writing an absolute value inequality from a graph?

• Determine the y-intercept

• Find the home base

• Identify the slope

• Calculate the area under the curve

How can you find the distance between two boundary values?

• By dividing the larger value by the smaller value

• By adding the values

• By subtracting the smaller value from the larger value

• By multiplying the values

Why might subtraction be used to find the distance between boundary values?

• To calculate the slope

• To find how far apart the values are

• To determine the midpoint

• To simplify the graph

What is the next step after finding the distance between boundary values?

• Cut the distance in half to find the midpoint

• Add the distance to the larger value

• Subtract the distance from the smaller value

• Multiply the distance by two

What is the significance of the midpoint in the context of the video?

• It is the lowest point on the graph

• It represents the highest point on the graph

• It is the average of the boundary values

• It is the home base for the inequality

What does the absolute value represent in this context?

• The difference between the boundary values

• The product of the boundary values

• The sum of the boundary values

• The distance from the home base

How do you incorporate the home base and distance into an inequality?

• By adding them together

• By subtracting the distance from the home base

• By using absolute value bars around the expression

• By multiplying them

How is the distance from the home base used in forming the inequality?

• It is placed outside the absolute value bars

• It is added to the home base

• It is subtracted from the home base

• It is multiplied by the home base