Understanding Absolute Value Equations

This video tutorial covers the concept of absolute value and how to solve absolute value equations. It begins with a review of absolute value as the distance from zero on a number line, emphasizing that it is always positive. The tutorial then explains how to solve absolute value equations, including those with expressions inside the absolute value. It also discusses scenarios where no solution exists, such as when the absolute value is set equal to a negative number. The video concludes with practice problems to reinforce the concepts learned.

What is the absolute value of a number?

• The number itself

• The distance from zero on a number line

• The negative of the number

• The square of the number

If the absolute value of -9 is calculated, what is the result?

• 18

• 9

• 0

• -9

What is the absolute value of -27?

• -27

• 0

• 27

• 54

How many solutions does the equation |x| = 3 have?

• Three

• None

• Two

• One

For the equation |x| = 3, what are the possible values of x?

• 3 and -3

• Only -3

• 0 and 3

• Only 3

What is the solution for the equation |x + 4| = 9?

• x = 0 and x = 9

• x = 5 and x = -13

• x = 9 and x = -9

• x = 13 and x = -5

If |x| = -5, what can be concluded?

• x = 0

• No solution

• x = -5

• x = 5

What is the result of solving |x - 7| = 18?

• x = 0 and x = 18

• x = 7 and x = -7

• x = 25 and x = -11

• x = 18 and x = -18

What is the solution for the equation |2x + 8| = 4?

• x = 6 and x = 2

• x = 0 and x = 4

• x = 2 and x = -2

• x = -6 and x = -2

When does an absolute value equation have no solution?

• When the absolute value equals infinity

• When the absolute value equals a positive number

• When the absolute value equals a negative number

• When the absolute value equals zero