Understanding Absolute Value Inequalities

The video tutorial explains how to solve a compound inequality involving the absolute value of x. It begins by introducing the problem and explaining the concept of absolute value as the distance from zero. A number line is used to visualize where x could be, considering two possible intervals. The tutorial then breaks down the inequality into two cases and applies additional constraints to find possible values for x. Finally, it concludes with a solution, demonstrating how to calculate the absolute value of x.

What does the absolute value of a number represent?

• The distance from zero

• The square of the number

• The number itself

• The negative of the number

In the context of the problem, what does the interval between 6 and 7 represent?

• Values of x squared

• Values of x

• Values of x - 3

• Values of x + 3

What are the two possible intervals for x - 3 based on the absolute value inequality?

• Between 6 and 7, and between -6 and -7

• Between 5 and 6, and between -5 and -6

• Between 7 and 8, and between -7 and -8

• Between 4 and 5, and between -4 and -5

What is the result of adding 3 to all parts of the inequality 6 < x - 3 < 7?

• 3 < x < 4

• 9 < x < 10

• 6 < x < 7

• 0 < x < 1

What constraint is applied to x in the problem?

• x is less than zero

• x is greater than zero

• x is not equal to zero

• x is equal to zero

Which interval is valid for x given the constraint x < 0?

• 0 < x < 1

• 6 < x < 7

• -4 < x < -3

• 9 < x < 10

What is one possible value of x that satisfies all conditions?

• -3.5

• 3.5

• 0

• 9.5

What is the absolute value of x if x = -3.5?

• 3.5

• 7

• -3.5

• 0

Why is the interval 9 < x < 10 ruled out?

• Because x must be greater than zero

• Because x must be less than zero

• Because x must be equal to zero

• Because x must be between 6 and 7

What is the final step in solving the problem?

• Finding the absolute value of x

• Drawing a number line

• Adding 3 to the inequality

• Applying the constraint x > 0