Final answer:
To determine the type of solution for an equation, solve the equation and analyze the result. If you find a unique value for the unknown, the solution is one solution. If you obtain a contradiction or an equation that is always false, the solution is no solution. If the equation is always true, the solution is infinite many solutions. If there is no equation or the equation is indeterminate, the solution is an empty set.
Step-by-step explanation:
In order to determine if the solution of an equation is one solution, no solution, empty set, or infinite many solutions (all real numbers), you need to solve the equation and analyze the result. Here are the steps:
- Determine the unknowns and knowns in the problem.
- Find an equation that expresses the unknown in terms of the knowns.
- Solve the equation or equations.
- Analyze the solution:
- If you find a unique value for the unknown, then the solution is one solution.
- If you obtain a contradiction or an equation that is always false, then the solution is no solution.
- If you end up with an equation that is always true, then the solution is infinite many solutions (all real numbers).
- If you have no equation or any equation that is indeterminate, then the solution is empty set.