While solving an equation, if the variable term becomes zero, and the equation makes a true statement, then the solution is one solution, no solution, or infinitely many solutions.
If the variable term becomes zero and the equation makes a true statement, then the equation reduces to a statement involving only constants.
- If this statement is true, then the original equation has infinitely many solutions. This is because any value of the variable will make the equation true, since the variable term no longer affects the truth of the equation.
- If this statement is false, then the original equation has no solutions. This is because the equation cannot be true when the variable term is zero, and no value of the variable can make it true.
In summary: if the variable term becomes zero and the equation is true, the solution is infinitely many; if the equation is false, the solution is no solution.