Solving Absolute Value Equations

This video tutorial covers solving absolute value equations. It begins with a review of absolute value concepts, emphasizing that absolute value represents the distance from zero and is always positive. The tutorial then progresses to simplifying expressions involving absolute values and solving both simple and complex absolute value equations. It also addresses scenarios where absolute value equations have no solution. Throughout the video, practice problems are provided to reinforce learning, and solutions are discussed to ensure understanding.

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 -5 is calculated, what is the result?

• 5

• 0

• 10

• -5

What does an absolute value equation represent?

• A division problem

• A multiplication problem

• A distance from zero

• A number's position on a graph

How many solutions can an absolute value equation have?

• Three

• Two

• One

• None

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

• x = 5 and x = -13

• x = 4 and x = -4

• x = 9 and x = -9

• x = 13 and x = -5

What happens if an absolute value equation equals a negative number?

• It has one solution

• It has two solutions

• It has no solution

• It has infinite solutions

In the equation |x - 7| = 18, what are the possible values of x?

• x = 11 and x = -25

• x = 25 and x = -11

• x = 18 and x = -18

• x = 7 and x = -7

What is the result of solving |x| = -21?

• No solution

• x = 0

• x = -21

• x = 21

If |x + 6| = 14, what are the solutions for x?

• x = 6 and x = -6

• x = 20 and x = -8

• x = 14 and x = -14

• x = 8 and x = -20

What should you do if an absolute value equation seems to have a solution but doesn't check out?

• Ignore the solution

• Recalculate the absolute value

• Check the solution again

• Assume it's correct