Question
Explain how to create an equation with infinitely many solutions. make the writing short
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Answered by
GPT-4o mini
To create an equation with infinitely many solutions, ensure both sides of the equation are equivalent. Here’s how:
1. **Start with a true statement**: For example, \(2x + 3 = 2x + 3\).
2. **Manipulate**: Rearrange or simplify without changing the equality, like \(2x + 3 - 2x = 3\) or \(0 = 0\).
3. **Generalize**: You can also use a variable that satisfies the equation, such as \(x = x\).
All such forms lead to infinitely many solutions, as any value for the variable satisfies the equation.
1. **Start with a true statement**: For example, \(2x + 3 = 2x + 3\).
2. **Manipulate**: Rearrange or simplify without changing the equality, like \(2x + 3 - 2x = 3\) or \(0 = 0\).
3. **Generalize**: You can also use a variable that satisfies the equation, such as \(x = x\).
All such forms lead to infinitely many solutions, as any value for the variable satisfies the equation.
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