Understanding Absolute Value Equations

The video tutorial explains how to solve absolute value equations by setting up two cases: one where the absolute value equals a positive number and another where it equals a negative number. It emphasizes that the absolute value of any number is always positive, making it impossible for an absolute value to equal a negative number. Therefore, if an absolute value equation equals a negative number, there is no solution.

What are the two cases considered when solving an absolute value equation?

• Absolute value equals a positive or zero

• Absolute value equals a negative or zero

• Absolute value equals zero or a positive number

• Absolute value equals a positive or negative number

What is the absolute value of a negative number?

• It is always zero

• It is always negative

• It is always positive

• It can be either positive or negative

Why is the absolute value of any number always positive?

• Because it represents the distance from zero

• Because it is always negative

• Because it is always zero

• Because it is a complex number

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

• There are two solutions

• There is one solution

• There are infinite solutions

• There is no solution

Can the absolute value of an expression ever be negative?

• No, never

• Only if the expression is zero

• Yes, sometimes

• Yes, always

What should you do if you encounter an absolute value equation equal to a negative number?

• Find the positive equivalent

• Solve for x

• Ignore the equation

• Conclude there is no solution