How to Determine When an Absolute Value Equation Has No Solution

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, the solution is 'no solution'.

What are the two cases considered when solving absolute value equations?

• One where the absolute value equals a negative number and another where it equals zero.

• One where the absolute value equals a positive number and another where it equals zero.

• One where the absolute value equals a positive number and another where it equals a negative number.

• One where the absolute value equals zero and another where it equals a positive number.

What is the absolute value of a negative number?

• It can be either positive or negative.

• It is always positive.

• It is always zero.

• It is always negative.

Why is it impossible for an absolute value to be negative?

• Because absolute values are always negative.

• Because absolute values can be either positive or negative.

• Because absolute values are always positive.

• Because absolute values are always zero.

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

• Ignore the negative case and solve for zero.

• Conclude that there is no solution.

• Solve for both positive and negative cases.

• Solve for the positive case only.

Which of the following statements is true about absolute values?

• The absolute value of a number can be negative.

• The absolute value of a number is always zero.

• The absolute value of a number is always positive.

• The absolute value of a number can be either positive or zero.