Question

Which of the following absolute value equations has no solution, and why?

A. |x| = 2
B. |x| = -1
C. |x| = 0
D. |x - 3| = 1

Answer 1

An absolute value equation has no solution if the absolute value expression is negative. Therefore, the absolute value equation with no solution is option B, |x| = -1.

Step-by-step explanation:

The absolute value of a number represents its distance from zero on a number line. An absolute value equation has no solution if the absolute value expression is negative. In this case, no matter what value we substitute for x, the absolute value expression will always be positive, so there is always a solution.

Therefore, the absolute value equation with no solution is option B, |x| = -1. This is because the absolute value of any number is always positive or zero, so it cannot equal a negative value.