Why is it necessary to apply inverse operations on both sides of the equals l sign when solving an equations

Take this example (cause it's easy to explain)

10+5x=15x

To solve it we have to minus five on both side. We have to do this because we need to isolate the variable (in this case x) on the one side so we can divide and solve.

You would -5x (inverse from positive 5) from both sides on this because whatever you do to one side you have to do to the others to make it equal. In this case the answer would be x=1 (again cause it's easy lol.)

I hope this helps you!