Question 409982
 In solving the equation (x + 1)(x – 2) = 54, Eric stated that the solution would be
x + 1 = 54 => x = 53
or
(x – 2) = 54 => x = 56
However, at least one of these solutions fails to work when substituted back into the original equation. Why is that? Please help Eric to understand better; solve the problem yourself, and explain your reasoning.
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We are told that (x+1)(x-2) = 54.

If x+1=54 then x-2 would have to equal 1 so the product could be 54
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Then x would have to be 53 and x would have to be 3 at the same time.
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But that is impossible.
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Your substitution reveals the contradiction very well.
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Cheers,
Stan H.
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