Exploring Absolute Value Equations and Inequalities

The video tutorial extends the previous lesson on absolute value equations and inequalities. It begins with solving basic absolute value equations, demonstrating how to translate them into two separate equations. The tutorial then progresses to solving absolute value inequalities, emphasizing the importance of switching inequality signs when dividing by negative numbers. Finally, it covers more complex inequalities, showing how to isolate variables and solve them on a number line.

What does it mean if the absolute value of an expression equals 7?

• The expression is 7 or -7

• The expression is greater than 7

• The expression is less than 7

• The expression is 0

If 2p - 3 equals 7, what is the value of p?

• 2

• 5

• 10

• 7

What happens to the inequality sign when you divide by a negative number?

• It becomes an equality

• It disappears

• It stays the same

• It switches direction

In the inequality |10 - 2k| ≥ 6, what are the two possible conditions for 10 - 2k?

• 10 - 2k > 6 or 10 - 2k < -6

• 10 - 2k ≥ 6 or 10 - 2k ≤ -6

• 10 - 2k = 6 or 10 - 2k = -6

• 10 - 2k ≤ 6 or 10 - 2k ≥ -6

How do you represent the solution of |10 - 2k| ≥ 6 on a number line?

• All numbers between 2 and 8

• All numbers less than or equal to 2 and greater than or equal to 8

• All numbers greater than 2 and less than 8

• All numbers between -2 and -8

What is the first step in solving the inequality 2|3k - 7| ≤ 8?

• Multiply by 2

• Divide by 2

• Subtract 11 from both sides

• Add 11 to both sides

After isolating the absolute value in 2|3k - 7| ≤ 8, what is the next step?

• Multiply by 2

• Subtract 7 from both sides

• Add 7 to both sides

• Divide by 2

What are the two conditions for the inequality |3k - 7| ≤ 4?

• 3k - 7 ≥ 4 and 3k - 7 ≤ -4

• 3k - 7 = 4 and 3k - 7 = -4

• 3k - 7 ≤ 4 and 3k - 7 ≥ -4

• 3k - 7 > 4 and 3k - 7 < -4

What is the solution for k in the inequality |3k - 7| ≤ 4?

• k ≤ 11/3 and k ≥ 1

• k ≥ 11/3 and k ≤ 1

• k > 11/3 and k < 1

• k = 11/3 and k = 1

How is the solution for k in |3k - 7| ≤ 4 represented on a number line?

• All numbers between -1 and -11/3

• All numbers greater than 1 and less than 11/3

• All numbers less than 1 and greater than 11/3

• All numbers between 1 and 11/3