To determine which equation among the listed options has no solution, let’s analyze each equation one by one:
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Equation 1: x + 3 = 5
Subtracting 3 from both sides, we get x = 2. This equation has a solution.
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Equation 2: 2x – 1 = 0
Adding 1 to both sides and then dividing by 2 gives x = 0.5. This equation also has a solution.
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Equation 3: 5 – 3x = 8
Rearranging this, we have -3x = 8 – 5, which simplifies to -3x = 3. Dividing by -3 results in x = -1. This equation has a solution.
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Equation 4: x + 9 = 0
Subtracting 9 from both sides gives x = -9. This equation has a solution as well.
However, if the original equations included more complex terms or were presented differently, it’s possible for an equation to have no solution. An example of an equation that has no solution is something like 2x + 3 = 2x + 5. In this case, when we subtract 2x from both sides, we are left with 3 = 5, which is clearly not true. Therefore, it has no solution.
In conclusion, among the provided equations, each has a solution, but it is essential to analyze equations carefully, as some formats can lead to no solutions.