Question

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. from an equation with variables on both sides has no solution. however, if 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 always has no solution or infinitely many solutions.

Explanation:

A is incorrect as an equation with variables on both sides may have one, many, or no solutions. B is incorrect because an equation with a variable only on one side can have no solution (e.g., 2 = 3). C is correct as when a variable is only on one side, we can isolate it to solve for it, assuming the equation is well - formed. D is incorrect as the presence of a variable on one side does not guarantee many solutions.

Answer:

C. If the variable only appears on one side of an equation, then the equation can always be solved for the variable.