Solving Absolute Value Inequalities

This video tutorial covers solving absolute value inequalities, building on previous lessons about absolute value equations. It explains the concept of absolute value as a distance from zero and demonstrates solving both equations and inequalities with examples. The tutorial also covers compound inequalities and special cases where solutions may not exist or include all real numbers.

What is the main focus of this lesson?

• Solving linear equations

• Solving absolute value inequalities

• Graphing quadratic functions

• Understanding complex numbers

What does the absolute value of a number represent?

• The negative of the number

• The number itself

• The square of the number

• The distance from zero on the number line

If |x| = 5, what are the possible values of x?

• 5 and -5

• 0 and 5

• Only -5

• Only 5

How do you solve |x| > 5?

• x > 5 or x < -5

• x < 5 and x > -5

• x = 5

• x = -5

What does interval notation help with?

• Expressing ranges of solutions

• Graphing functions

• Solving equations

• Finding derivatives

How do you express |x| < 7 using inequalities?

• x > 7 or x < -7

• x = 7

• -7 < x < 7

• x = -7

What is the solution to |ax + b| > k?

• ax + b > k and ax + b < -k

• ax + b > k or ax + b < -k

• ax + b = k

• ax + b < k

What is the graphical representation of |x| < 5?

• A line from -infinity to -5

• A line from 5 to infinity

• A point at 5

• A line from -5 to 5, not including -5 and 5

What happens if an absolute value inequality is less than a negative number?

• It has one solution

• It has no solution

• It has two solutions

• It has infinite solutions

What is the solution to |10x + 1| > -15?

• x < -15

• x > 15

• All real numbers

• No solution