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

by coverband
Tags: 3<7, 3|<7, 5<x, imply
 P: 167 If 5
P: 1,635
 Quote by coverband If 5
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?
 P: 1,635 also, i do not think it is right to say 5
P: 167

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

I know its just my analysis notes that subject is so weird the lecturer writes things down that don't make sense and then looks at you like you've got ten heads when you question it. Weird subject man
 P: 167 "also, i do not think it is right to say 5
 P: 167 Also if |x-3| < A/|x+3| we need to bound |x+3| right? Now if you take |2/3x||x-1/2| < A why do we bound |2/3x| and not |3x/2| ?
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Emeritus
P: 38,430
 Quote by coverband I know its just my analysis notes that subject is so weird the lecturer writes things down that don't make sense and then looks at you like you've got ten heads when you question it. Weird subject man
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.
P: 461
 Quote by sutupidmath also, i do not think it is right to say 5
The linguistic convention in math is that "A implies B' means precisely that there is no case when A holds and B doesn't.
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P: 38,430
 Quote by sutupidmath also, i do not think it is right to say 5
?? 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.
P: 1,635
 Quote by HallsofIvy ?? 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!
P: 167
 Quote by HallsofIvy If 5< x+ 3< 7 then it is certainly true that -7< x+ 3< 7 so |x+3|< 7.
But in the first one 2<x<4, in the second one -10<x<4
 P: 107 well if x is greater than two it's certainly greater than 10...
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P: 38,430
 Quote by matticus well if x is greater than two it's certainly greater than 10...
!!!! Oh, wait, that was a typo. "greater than -10".
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