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Which of the following equations does not have at least one

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by Frankenstein » Thu Jul 07, 2011 6:41 am
Hi,
B,C,D,E are all linear equations in one variable and they have 1 solution. There is no variable in A as both sides are same.

Hence, A
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by Ian Stewart » Thu Jul 07, 2011 10:00 am
saxenashobhit wrote:Which of the following equations does not have at least one solution?

(-3)-x = -3-x

(-3)x = (-3)-x

(-3)- x = -3x

3-x = (-3)x

3x = (-3)-x
This question makes absolutely no sense. Clearly B, C, D and E have *exactly* one solution for x. The equation in A is different; if we just remove the brackets, we have:

-3 - x = - 3 - x

which is obviously true for *every* value of x, since the left and the right side are the same. So this equation has an infinite number of solutions, and certainly also has 'at least one solution'. Every answer choice is good here. A would only be right if, when you simplified, you got something like "0=1", or some other mathematical impossibility. In that case, the equation would be impossible, and thus would have no solutions: an equation like x = x + 1 has absolutely no solutions, for example. But as the question is written, the answer is 'F', none of the above.
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