Exploring Absolute Value Inequalities in Algebra

The video tutorial covers solving inequalities involving absolute values, a topic often found confusing in algebra. It begins with a simple problem, explaining the concept of absolute value as the distance from zero. The tutorial progresses to more complex inequalities, emphasizing visualization with number lines and avoiding memorization of rules. It explains how to set up and solve compound inequalities, providing examples and correcting mistakes. The video aims to make understanding absolute value inequalities intuitive through practice and visualization.

What is the range of x for the inequality |x| < 12?

• x > -12 only

• x < 12 only

• -12 <= x <= 12

• -12 < x < 12

What does the absolute value of a number represent?

• Its distance from 0

• Its negative value

• Its positive value

• Its square root

What is the correct interval notation for the solution of |x| < 12?

• (12, -12)

• [-12, 12]

• (-12, 12)

• [-12, -12]

For the inequality |7x| >= 21, what are the possible values of x?

• x = 3 only

• -3 < x < 3

• x < -3 or x > 3

• x <= -3 or x >= 3

What is the solution set for |7x| >= 21?

• x >= 3 or x <= -3

• x > 3 or x < -3

• 3 <= x <= -3

• x = 3 or x = -3

How is the inequality |5x + 3| < 7 solved?

• x < -2 or x > 4/5

• x > -2 and x < 4/5

• x >= -2 or x <= 4/5

• x <= -2 and x >= 4/5

How do you solve an inequality like |5x + 3| < 7?

• By splitting it into two separate inequalities

• By squaring both sides

• By adding 7 to both sides

• By taking the square root of both sides

In the context of absolute value inequalities, what does it mean if |f(x)| < a?

• f(x) equals a

• f(x) is more than a units away from 0

• f(x) is exactly a units away from 0

• f(x) is less than a units away from 0

For the inequality |2x/7 + 9| > 5/7, which of the following is true?

• x > -29 or x < -34

• x >= -29 or x <= -34

• x > -29 and x < -34

• -29 < x < -34

What does it mean if |f(x)| > a in the context of absolute value inequalities?

• f(x) is less than a units away from 0

• f(x) is exactly a units away from 0

• f(x) is more than a units away from 0

• f(x) equals a