Understanding Absolute Value Equations

The video tutorial explains how to solve absolute value equations by creating two cases: one for the positive value and one for the negative value. It demonstrates the step-by-step process of solving these equations and emphasizes the importance of checking solutions to avoid extraneous results. The tutorial provides a clear understanding of the concept and ensures that students can verify their solutions effectively.

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

• Multiply both sides by a constant

• Add a constant to both sides

• Consider the two cases for the absolute value

• Subtract a constant from both sides

When solving 2x - 1 = 5, what is the other equation you need to consider?

• 2x - 1 = 1

• 2x - 1 = 0

• 2x - 1 = -5

• 2x - 1 = 10

What operation is performed after adding 1 to both sides of the equation 2x - 1 = 5?

• Multiply by 2

• Subtract 2

• Divide by 2

• Add 2

Why is it important to check solutions in absolute value equations?

• To find the exact value of x

• To ensure there are no extraneous solutions

• To verify the equation is linear

• To simplify the equation further

What is an extraneous solution?

• A solution that does not satisfy the equation

• A solution that satisfies the equation

• A solution that is greater than zero

• A solution that is less than zero

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

• By checking if the solution is positive

• By graphing the equation

• By substituting the solution back into the original equation

• By solving the equation again

What is the result of substituting x = 3 into the equation 2x - 1?

• 7

• 6

• 5

• 4

What is the absolute value of -5?

• 10

• 5

• 0

• -5

What is the result of substituting x = -2 into the equation 2x - 1?

• -5

• -3

• -9

• -7

What is the absolute value of 5?

• 5

• 0

• 10

• -5