Question

Is it possible for an inequality to have exactly one solution? Exactly two solutions? Why or why not?(no absurd please)

Answer 1

Answer:

Yes

Step-by-step explanation:

Consider the inequalities in one variable.

For strict inequalities (inequalities involving > and <), you either have infinitely many solutions or no solution, but for inequalities involving >= or <=, then you can have exactly 1, 2 or any number of solutions.

For example, x² <= 0 has exactly one real solution of x=0, because x² is always nonnegative for real x, and is 0 only when x=0. Similarly, x²(x-1)² <= 0 has exactly two real solutions of x=0 or x=1, as you can rewrite the inequality into [x(x-1)]²<=0, and the square implies the whole expression is nonnegative for real x, and is equal to 0 only when x(x-1)=0, i.e. x=0 or x=1.