Solving Absolute Value Inequalities Challenge

The video tutorial covers solving absolute value inequalities, focusing on 'and' and 'or' inequalities. It explains how to treat inequalities with less than as 'and' compound inequalities and those with greater than as 'or' inequalities. The tutorial provides examples of solving absolute value inequalities, demonstrating the process on a number line and explaining the importance of flipping the sign when dealing with negative cases. The video also includes examples of solving inequalities with both greater than and less than symbols, emphasizing the steps to isolate the absolute value and solve the inequalities.

What type of inequality is represented by 'less than' in absolute value inequalities?

• A simple inequality

• A compound inequality

• An 'and' inequality

• An 'or' inequality

How do you represent an 'or' inequality in absolute value inequalities?

• By using a semicolon

• By using a comma

• By using the word 'or'

• By using the word 'and'

If the absolute value of x is greater than 3, which of the following is a correct solution?

• x > 3 or x < -3

• x < 3 and x > -3

• x < 3 or x > -3

• x > 3 and x < -3

What happens to the inequality sign when you create the negative case in an absolute value inequality?

• It flips

• It becomes an 'or' inequality

• It stays the same

• It becomes an 'and' inequality

When solving the absolute value of 3x + 6 is greater than or equal to 12, what is the first step?

• Multiply by 3

• Divide by 3

• Subtract 6 from both sides

• Add 6 to both sides

In the inequality 3x + 6 is less than or equal to -12, what is the next step after subtracting 6 from both sides?

• Subtract 3 from both sides

• Divide by 3

• Multiply by 3

• Add 6 to both sides

What type of inequality is represented by 'greater than or equal to' in absolute value inequalities?

• A simple inequality

• An 'and' inequality

• An 'or' inequality

• A compound inequality

When solving the absolute value of 2x + 6 is less than 8, what is the first step?

• Divide by 3

• Add 6 to both sides

• Subtract 6 from both sides

• Multiply by 3

In an 'and' inequality, how can you represent the solution?

• As a simple inequality

• As a compound inequality

• As one combined inequality

• As two separate inequalities

What is the solution to the inequality -14 < 2x + 6 < 8 after subtracting 6 from all parts?

• -14 < 2x < 2

• -20 < 2x < 14

• -20 < 2x < 2

• -8 < 2x < 2