Since you ask about the source of my exasperation it comes down to a single thing. You are not just a naive questioner. You have asked a question, you have gotten an answer that should have been sufficient. You did not like the answer that you got. So rather than expending your own effort to understand the answer and learn more, you skulk off to another board to ask the same question expecting a different answer. You should try and learn to crawl and walk before you try to run a marathon.
To modulate means to combine two things which are both changing. This combination process is generally non-linear. Multiplication is a non-linear process. In Amplitude Modulation(AM) two signals are combined in a multiplier. If you know trigonometry you can work out that if you multiply two sine waves of different frequencies, call them f1 and f2, you will get four different signals out. The four outputs will be at frequencies f1, f2, f1 + f2, f1 - f2. The signals at the sum of the two frequencies and the difference of the two frequencies are called sidebands. Once you understand AM modulation you can tackle Frequency Modulation(FM). The detailed math is a bit harier and involves Bessel functions.
In your original example the 7.49 MHz. signal was not changing, and it could not be a modulating signal. FM does not mean that you change one frequency with another frequency. Typically FM uses the amplitude of the voice to change the frequency of the carrier. In order to modulate the 88.1 MHz carrier you have to have something that changes. Using voice to modulate an FM carrier, it is the amplitude of the voice that changes the frequency. Understandable speech has a bandwidth of 3kHz. In a narrow band FM transceiver the 3kHz. bandwidth creates an FM modulated output with a much wider bandwidth, as much as 25 kHz. An FM broadcast station which wants to produce high fidelity music to 20 KHz. is spaced 200 KHz. from nearby stations to avoid interference. FM modulation consumes way more bandwidth than the modulating signal.