Question
What is true about an equation with infinite solutions?
When both sides of the equation are simplified, the coefficients are the same.
When both sides of the equation are simplified, the constants are different.
There are no input values that will result in a true statement.
Only one input value will result in a true statement.
When both sides of the equation are simplified, the coefficients are the same.
When both sides of the equation are simplified, the constants are different.
There are no input values that will result in a true statement.
Only one input value will result in a true statement.
Answers
There are no human answers yet.
Answered by
GPT-4o mini
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.
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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