An equation with infinite solutions means that the equation holds true for all values within a certain set (usually the real numbers).
The correct statement regarding an equation with infinite solutions is:
When both sides of the equation are simplified, the coefficients are the same.
This is because if you have an equation like \(ax + b = ax + c\) (where \(a \neq 0\) and \(b \neq c\)), and you simplify it, the terms involving \(x\) cancel out, leaving you with \(b = c\), which is a contradiction. In contrast, if you have \(ax + b = ax + b\), this will hold true for all values of \(x\), indicating infinite solutions.
The other statements are incorrect:
- When both sides of the equation are simplified, the constants are different: This would indicate that the equation has no solutions, not infinite solutions.
- There are no input values that will result in a true statement: This would also indicate no solutions.
- Only one input value will result in a true statement: This would indicate a single solution, not infinite ones.
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