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

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

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- #1

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

- #2

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well |x+3|<7 implies thatIf 5<x+3<7 does this imply |x+3|<7 ??

-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?

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- #5

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Thanks i think

- #6

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Now if you take |2/3x||x-1/2| < A why do we bound |2/3x| and not |3x/2| ?

- #7

HallsofIvy

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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.

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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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HallsofIvy

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?? 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.

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

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But in the first one 2<x<4, in the second one -10<x<4If 5< x+ 3< 7 then it is certainly true that -7< x+ 3< 7 so |x+3|< 7.

- #12

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

- #13

HallsofIvy

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!!!! Oh, wait, that was a typo. "greater than -10".well if x is greater than two it's certainly greater than 10...

- #14

HallsofIvy

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That's why it isBut in the first one 2<x<4, in the second one -10<x<4

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