Solve and graph an absolute value inequality with no solution

The video tutorial explains how to solve and graph linear and absolute value inequalities. It begins by isolating the absolute value in the equation and setting up two scenarios to solve it. The instructor emphasizes the importance of understanding that absolute values represent distance from zero, which cannot be negative. Therefore, if an absolute value inequality results in a negative number, it has no solution. The tutorial concludes by reinforcing that any isolated absolute value inequality with a negative result is unsolvable.

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

• Graph the inequality

• Isolate the absolute value

• Add a constant to both sides

• Multiply both sides by a negative number

Why do we set up two scenarios when solving absolute value inequalities?

• To account for both positive and negative solutions

• To simplify the equation

• To eliminate the absolute value

• To find the maximum and minimum values

What does the absolute value of a number represent?

• The number itself

• The negative of the number

• The distance from zero

• The square of the number

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

• Because it is always negative

• Because it is always zero

• Because it is always positive

• Because it represents a distance, which cannot be negative

What conclusion can be drawn if an absolute value inequality results in a negative number?

• The inequality has multiple solutions

• The inequality is always false

• The inequality is always true

• The inequality has no solution