Question

Give a unique example of each:
1. An absolute value equation with two solutions
2. An absolute value equation with one solution
3 An absolute value equation with no solutions



would |x - 1| = 10

|x| = 0

|x - 1| = -10 work ?

Answer 1

The first two are correct, the third however is a little tricky. Since the absolute value of any function cannot be negative the equation that you formed is flawed in the basis of its formation and hence does not have solution. If it was about getting 'real' solution only, then you could also use a quadratic equation with imaginary (complex) roots inside the absolute value function (roots are imaginary for quadratic equations with D<0).