Question

it means that the equation has exactly one solution.
it means that the equation has infinitely many solutions.
it means that there are no values of the variable that can satisfy the equation.
it means that the equation has two solutions.
what does it mean if an absolute value equation has no solution?

Explanation:

An absolute value equation \( |x| = a \). If \( a<0 \), there are no values of the variable that can satisfy the equation because the absolute value of a number (by definition \( |y|=

$$\begin{cases}y, & y\geq0\\-y, & y < 0\end{cases}$$

\)) is always non - negative (\( |y|\geq0 \) for all real \( y \)). For example, the equation \( |x|=- 2 \) has no solution since no real number \( x \) will make the left - hand side (which is non - negative) equal to a negative number.

Answer:

It means that there are no values of the variable that can satisfy the equation.