Answer:
Step-by-step explanation:
A. Every equation with variables on both sides has no solution. However, it is also possible for an equation with the variable on only one side to also have no solution.
- False, the first pat incorrect. The equation can be simplified to have variable on one side and solved further.
B. If the variable only appears on one side of an equation, then the equation can always be solved for the variable. This means that if an equation has no solution, then the variable must appear on both sides.
- False, the second part is incorrect. If an equation has no solution, then variables disappear and it results in nonsense equation.
C. Any equation can have one solution, infinitely many solutions, or no solutions. This does not depend on whether the variable appears on only one side or on both sides.
D. If the variable only appears on one side of an equation, then the equation can always be solved for the variable. By contrast, an equation with variables on both sides always has no solution or infinitely many solutions.
- False, the second part is incorrect. The variables can be taken to the same side of equation. If they cancel and leave a correct equation, then it results in infinitely many solutions. If they cancel and leave incorrect equation, then it results in no solution. If it simplifies with variable on one side, then there is one solution.
