OP is talking about this one.
Coming to the question, the explanation is right.
Consider y = 0. In this example, y can be 0, in two ways. Either 5x + 4 is 0 or 2x - 3 is 0. In the first case, x = -4/5. In the second, x = 3/2. Thus, for two x-values, y has the same value 0. This isn't possible with injective functions.