In solving the equation (x + 4)(x – 7) = -18, Eric stated that the solution would be x + 4 = -18 => x = -22 or (x – 7) = -18 => x = -11 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 Solution You cannot separate the factors x + 4 and x - 7 unless the product is 0! (x + 4)(x - 7) = -24 x^2 - 3x - 28 = -24 x^2 - 3x - 4 = 0 (x - 4)(x + 1) = 0 Now you can separate the factors!! x - 4 = 0 or x + 1 = 0 x = 4...............x = -1 .

1. In solving the equation (x + 4)(x – 7) = -18, Eric stated that the solution would be
x + 4 = -18 => x = -22
or
(x – 7) = -18 => x = -11
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
Solution
You cannot separate the factors x + 4 and x - 7 unless the product is 0! (x + 4)(x - 7) = -24 x^2 -
3x - 28 = -24 x^2 - 3x - 4 = 0 (x - 4)(x + 1) = 0 Now you can separate the factors!! x - 4 = 0 or x
+ 1 = 0 x = 4...............x = -1