We are given the following absolute value equation and we need to describe for what values of c the equation has no solution.
|x-7|= c
Notice that we do not need to solve this equation. All we need to do is to think about the absolute value itself. Absolute value takes a number or an expression as an input and gives a non-negative value as an output. In other words, |x-7| cannot be less than 0.
|x-7|≥0
This restricts the values of c to be non-negative if we want our equation to have a solution. Therefore, the given equation has no solution if c<0.
