Understanding Absolute Value Inequalities

The video tutorial explains how to write and solve an absolute value inequality. It begins by graphing the solution set and identifying key points such as the midpoint and distance. The tutorial then demonstrates how to formulate the inequality and solve it, ensuring the solution matches the graph. Finally, it generalizes the process for writing absolute value inequalities, explaining the conditions under which inequalities diverge or converge.

What is the first step in writing an absolute value inequality for a given solution set?

• Graph the solution set.

• Identify the midpoint of the solution set.

• Solve the inequality.

• Calculate the distance between the points.

In the graphical representation, what do the open circles at -3 and 9 indicate?

• The points are excluded from the solution set.

• The points are included in the solution set.

• The points are the endpoints of the solution set.

• The points are the midpoint of the solution set.

How do you find the midpoint between two numbers?

• Add the numbers and divide by 2.

• Subtract the smaller number from the larger number.

• Multiply the numbers and take the square root.

• Divide the larger number by the smaller number.

What is the midpoint between -3 and 9?

• 6

• 3

• 0

• 9

What is the distance from the midpoint to each endpoint in the solution set?

• 9

• 6

• 12

• 3

How is the absolute value inequality formulated using the midpoint and distance?

• x + midpoint < distance

• x - midpoint < distance

• x + midpoint > distance

• x - midpoint > distance

What does the inequality x - 3 > 6 represent?

• x is greater than 9

• x is less than -3

• x is less than 9

• x is greater than -3

What does the inequality x - 3 < -6 represent?

• x is less than 9

• x is greater than -3

• x is greater than 9

• x is less than -3

What is the solution set for the inequality x - 3 > 6 or x - 3 < -6?

• x > 3 and x < 6

• x > -3 and x < 9

• x < 3 or x > 6

• x < -3 or x > 9

Why is the solution set x < -3 or x > 9 correct?

• Because the inequalities go towards each other.

• Because the inequalities go away from each other.

• Because the inequalities are equal.

• Because the inequalities are less than each other.