To infer means to conclude or to draw a conclusion. To imply means to hint or to suggest. Thus, audiences (those receiving a message) infer while communicators (those sending out a message) imply. Accordingly, a savvy writer will adjust the sentence in the example graphic to look more like this:
Remembering the roles that to infer and to imply may legitimately play based on their definitions can help steer a writer clear of imprecise writing. To infer means to conclude, which can be done by the receiver of a message and not the sender. To imply means to hint or to suggest, which can be done by the sender and the receiver. Thus, just as messages are received from the sender, infer to draw conclusions, but imply to hint or suggest.