If 5<x+3<7 does this imply |x+3|<7 ?

well |x+3|<7 implies that

-7<x+3<7, which means that -10<x<4

now you have 5<x+3<7
which means that 2< x<4, so what do u think now?

 

also, i do not think it is right to say 5<x+3<7, implies |x+3|<7, but rather when the first holds true, also the second will hold true. the vice versa does not hold true.

 

Why do you consider that weird or that it doesn't make sense? Frankly when I read your first post I thought it was by a student in an algebra or pre-calculus class. Yes, I can imagine a teacher, in an analysis class who had written "if 5<x+3<7 then |x+3|<7", thinking "Oh, my god, am I going to have to go back and teach basic algebra?" if a student questioned it.

If 5< x+ 3< 7 then it is certainly true that -7< x+ 3< 7 so |x+3|< 7.

 

The linguistic convention in math is that "A implies B' means precisely that there is no case when A holds and B doesn't.

 

?? That is exactly what "implies" means. "A implies B" means that whenever A is true, B is also true. It does NOT mean that the converse, "If B is true then A is true" holds.

 

Really!!!! It might be because of my english not being my first language then! sorry, my bad!

 

well if x is greater than two it's certainly greater than 10...

 

!!!! Oh, wait, that was a typo. "greater than -10".

 

That's why it is not a "biconditional". 2< x< 4 implies -10< x< 4 (because -10< 2) but the other way is not true.