Question

do only equations with variables on both sides have two solutions? or can the variable be just on one side? justify your answer. choose the correct answer below. a. 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. b. 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. c. 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. 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 might have no solution.

Explanation:

An equation with variables on both sides may have one solution, infinitely many solutions, or no solutions. It depends on the coefficients and constants of the equation. If a variable only appears on one - side of an equation, it can potentially be solved for that variable. But having a variable on one side doesn't guarantee a solution exists. And having variables on both sides doesn't mean there can't be a solution.

Answer:

None of the options (A - D) are entirely correct. An equation with variables on both sides can have one solution, infinitely many solutions, or no solutions. If a variable only appears on one side of an equation, it may or may not be solvable depending on the nature of the equation.