Question

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 1

It doesn't work because if we assume:

x+3 = 48

we fail to take into account the x+1 expression.

However, if we had the equation (x+3)(x+1) = 0, then we can set x+3 = 0

Answer 2

It doesn't work because

ab = 48 does not mean that one or the other is 48.

However, if ab=0, then one or the other must be 0.