x²<9 and 1-2x<7. They are for two DIFFERENT cases. What is the point of adding together inequalities from completely different situations?
Why can't you add inequalities ,coming from completely different situations??
Because they have nothing to do with one another. That's like saying "why can't you apply the Pythagorean theorem to things which aren't triangles" It's because the theorem is a statement about triangles, so you HAVE to have a right triangle to use it. Similarly, if 0<x<3 AND -3<x<0, then there is NO x for which this is true, so you're not proving anything at all, rather you're proving that for all nonexistent x your statement is true, and who cares about that, you're aiming to prove it for |x|<3, and those x actually exist.
So in my proof ,which law of logic ,theorem,definition or axiom is ,do you think is violated??
Also in my proof i did not add 0<x<3 and -3<x<0 ,but add
1-2x<7 . Now there is an x satisfying those two inequalities