Exploring Absolute Value Equations and Inequalities

The video tutorial covers solving and graphing absolute value equations and inequalities. It explains the concept of absolute value as a distance from zero and demonstrates how to solve equations by considering both positive and negative solutions. The tutorial also addresses graphing inequalities, identifying no-solution scenarios, and applying these concepts to real-world problems, such as nutritional supplement intake. Additionally, it emphasizes the importance of checking solutions to avoid extraneous results.

What is the absolute value of -14?

• 28

• 14

• 0

• -14

Which of the following is a solution to the equation |x| = 14?

• x = -14

• x = 14

• Both B and C

• x = 0

In an absolute value inequality, what does a 'greater than' inequality represent?

• A conjunction

• A contradiction

• A disjunction

• An equation

How do you solve the inequality |x + 3| > 6?

• x + 3 = -6

• x + 3 = 6

• x + 3 > -6 and x + 3 < 6

• x + 3 < -6 or x + 3 > 6

What is the solution to the equation |8n - 3| = -2?

• n = 2

• n = -2

• No solution

• n = 0

What are the solutions to the equation |4y - 6| = 5?

• y = -1/4 and y = -11/4

• y = 1/4 and y = -11/4

• y = 1/4 and y = 11/4

• y = -1/4 and y = 11/4

How do you graph the inequality |x| < 5?

• Closed circles at -5 and 5

• Open circles at -5 and 5

• Open circles at -5 and 5 with shading in between

• Closed circles at -5 and 5 with shading in between

If a skater's distance from you is given by |100 - 20t|, at what times is she 20 feet away?

• t = 2 and t = 4

• t = 4 and t = 6

• t = 1 and t = 7

• t = 3 and t = 5

What is the range of daily intake if the recommended amount is 1100 mg with a tolerance of ±150 mg?

• 850 to 1350 mg

• 900 to 1300 mg

• 1000 to 1200 mg

• 950 to 1250 mg

Which of the following is an extraneous solution for the equation |x + 15| = 4x?

• x = -3

• x = 5

• x = 3

• x = -5