How Many solutions? Quick Check

Question

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

Answer 1

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.