Answer
If an equation is true for one value it means that equation has one solution. If an equation is not true for any value, this means that equation has no solution. And if an equation is true for any real number substituted in the equation, this means that equation has infinitely many solutions.
Work Step by Step
If an equation is true for one value it means that equation has one solution. If an equation is not true for any value, this means that equation has no solution. And if an equation is true for any real number substituted in the equation, this means that equation has infinitely many solutions.
An equation is formed when two algebraic expressions are equated with equal sign. An equation uses variables to express the relationship between two or more quantities.
There can be many equations which have no solution set at all. There can be many equations which may have finite/infinite many solutions. And there can be many equations which have same solution set.
Example:
Suppose there is provided an algebraic equation.
When attempt to solve this equation, it is find that this equation is true for one value only say\[x=4\], this means the provided equation has only one solution in its solution set.
Again, when attempt to solve this equation, it is find that this equation is not true even for any single value say result is like \[3=7\], this means the provided equation has no solution in its solution set.
Next, if attempt to solve this equation, it is find that this equation is true for any real number substituted in the equation such as \[2=2\], this means the provided equation has infinitely many solutions in its solution set.
