Question
How Many solutions? Quick Check
Which of the following is an example of an equation with no solution?(1 point)3x+4=3x+3
3 x plus 4 equals 3 x plus 3
plus 4 equals 3 x plus 4
3x+4=4x+3
3 x 4x+3=3x+3
Which of the following is an example of an equation with no solution?(1 point)3x+4=3x+3
3 x plus 4 equals 3 x plus 3
plus 4 equals 3 x plus 4
3x+4=4x+3
3 x 4x+3=3x+3
Answers
GPT-4o mini
To determine which of the equations has no solution, let's analyze each option:
1. **3x + 4 = 3x + 3**: Subtracting 3x from both sides gives us \(4 = 3\). This is a false statement, indicating there are no solutions.
2. **3 + 4 = 3x + 4**: This appears to be a typographical error, but if we assume it means \(3 + 4 = 3x + 4\), simplifying gives \(7 = 3x + 4\) or \(3x = 3\), which has solutions.
3. **3x + 4 = 4x + 3**: Subtracting \(3x\) and \(4\) gives \(0 = x - 1\) or \(x = 1\), indicating there is a solution.
4. **3x = 3x + 3**: Subtracting \(3x\) from both sides gives us \(0 = 3\), a false statement, indicating no solutions.
Based on this analysis, the equations with no solutions are **1. 3x + 4 = 3x + 3** and **4. 3x = 3x + 3**. If you're looking to choose only one specific option listed, then **3x + 4 = 3x + 3** fits as an example of an equation with no solution.
1. **3x + 4 = 3x + 3**: Subtracting 3x from both sides gives us \(4 = 3\). This is a false statement, indicating there are no solutions.
2. **3 + 4 = 3x + 4**: This appears to be a typographical error, but if we assume it means \(3 + 4 = 3x + 4\), simplifying gives \(7 = 3x + 4\) or \(3x = 3\), which has solutions.
3. **3x + 4 = 4x + 3**: Subtracting \(3x\) and \(4\) gives \(0 = x - 1\) or \(x = 1\), indicating there is a solution.
4. **3x = 3x + 3**: Subtracting \(3x\) from both sides gives us \(0 = 3\), a false statement, indicating no solutions.
Based on this analysis, the equations with no solutions are **1. 3x + 4 = 3x + 3** and **4. 3x = 3x + 3**. If you're looking to choose only one specific option listed, then **3x + 4 = 3x + 3** fits as an example of an equation with no solution.