Question 644953: In solving the equation (x + 3)(x + 1) = 48, Eric stated that the solution would be
x + 3 = 48 => x = 45
or
(x + 1) = 48 => x = 47
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.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! In solving the equation (x + 3)(x + 1) = 48, Eric stated that the solution would be
x + 3 = 48 => x = 45
or
(x + 1) = 48 => x = 47
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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Although the product of the 2 factos is 48, one of the factors does
not have to be 48. The factors could be 6 and 8, or 2 and 24, or
any other combinations factors whose product is 48.
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Solution:
(x+3)(x+1) = 48
x^2 + 4x + 3 = 48
x^2 + 4x - 45 = 0
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Factor
x^2 + 9x-5x - 45 = 0
Factor:
x(x+9) -5(x+9) = 0
(x+9)(x-5) = 0
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Since this product is zero, at least one of those factors
MUST be zero.
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x+9 = 0 OR x-5 = 0
x = -9 OR x = 5
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Cheers,
Stan H.
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