To determine which equation has no solution, let’s analyze each one:
- Equation 1: x + 3 = 5
Subtracting 3 from both sides gives us x = 2. This has a solution. - Equation 2: 2x – 1 = 0
Adding 1 to both sides results in 2x = 1. Dividing by 2, we find x = 0.5. This also has a solution. - Equation 3: 5 – 3x = 8
Rearranging gives us -3x = 8 – 5, or -3x = 3. Dividing by -3, we find x = -1. This has a solution. - Equation 4: x + 9 = 0
Subtracting 9 from both sides gives us x = -9. This has a solution.
All four equations have solutions. However, if we modify one of these equations slightly, we could create one that has no solution. For example, equations like 2x + 1 = 0 and 2x + 3 = 0 will not yield valid solutions if set equal to a contradictory statement such as 1 = 0.
In conclusion, among the given equations, all have solutions. Therefore, without additional context or adjustments to an equation, none of them can be said to have no solution.