Final answer:
Equations with variables on both sides can result in one solution, no solution, or infinitely many solutions. The exact nature of the solutions can be determined by simplifying the equation.
Step-by-step explanation:
Equations that have variables on both sides can have one of three different solutions. These are:
- One solution: This is when the equation can be simplified to yield a unique value for the variable, indicating that there is exactly one solution to the equation.
- No solution: Sometimes, after simplifying the equations, you may end up with a statement that is never true (such as 0 = 1), which indicates that there is no possible value for the variable that can satisfy the equation.
- Infinitely many solutions: In some cases, the simplification process results in a true statement for any value of the variable (like 0 = 0), indicating that any real number could be a solution, hence the equation has infinitely many solutions.
When an equation includes an unknown squared, it typically indicates a quadratic equation, which often has two solutions. However, determining the exact number and type of solutions requires inspecting the equation post-simplification.