Understanding Absolute Value Equations

The video tutorial explains how to solve absolute value equations by isolating the absolute value, setting up two equations, and solving them. It demonstrates the process with two examples, verifying solutions for accuracy. The tutorial emphasizes understanding the principle that absolute values can equal both positive and negative numbers, leading to two potential solutions for each equation.

What is the first step in solving an absolute value equation?

• Check the solutions

• Set up two equations

• Isolate the absolute value

• Multiply both sides by a constant

When solving the equation |x + 4| = 5, what are the two possible equations you can set up?

• x + 4 = 0 and x + 4 = -5

• x + 4 = 5 and x + 4 = -5

• x + 4 = 5 and x + 4 = 10

• x + 4 = 5 and x + 4 = 0

What is the solution for x in the equation x + 4 = 5?

• x = 9

• x = 1

• x = -1

• x = -9

How do you verify if a solution to an absolute value equation is correct?

• By graphing the equation

• By checking if it satisfies the original equation

• By solving the equation again

• By substituting into a different equation

What is the first step in solving the equation |3x - 1| - 9 = 4?

• Subtract 9 from both sides

• Add 9 to both sides

• Multiply both sides by 3

• Divide both sides by 3

What are the two equations derived from |3x - 1| = 13?

• 3x - 1 = 13 and 3x - 1 = -13

• 3x - 1 = 13 and 3x - 1 = 26

• 3x - 1 = 13 and 3x - 1 = 0

• 3x - 1 = 0 and 3x - 1 = -13

What is the solution for x in the equation 3x - 1 = 13?

• x = 14/3

• x = 4

• x = 5

• x = 3

What is the solution for x in the equation 3x - 1 = -13?

• x = -14/3

• x = -5

• x = -3

• x = -4

Why do we set up two equations when solving an absolute value equation?

• To make the equation easier to solve

• Because there are two possible values for the absolute value

• To check for errors

• To find the average of the solutions

What should you do after finding the solutions to an absolute value equation?

• Ignore the solutions

• Graph the solutions

• Verify the solutions

• Multiply the solutions