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

1. Feb 7, 2008

### coverband

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

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

2. Feb 7, 2008

### sutupidmath

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?

3. Feb 7, 2008

### sutupidmath

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.

4. Feb 7, 2008

### 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

5. Feb 7, 2008

### coverband

"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."

Thanks i think

6. Feb 7, 2008

### coverband

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| ?

7. Feb 7, 2008

### HallsofIvy

Staff Emeritus
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.

8. Feb 7, 2008

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

9. Feb 7, 2008

### HallsofIvy

Staff Emeritus
?? 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.

10. Feb 7, 2008

### sutupidmath

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

11. Feb 7, 2008

### coverband

But in the first one 2<x<4, in the second one -10<x<4

12. Feb 7, 2008

### matticus

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

13. Feb 7, 2008

### HallsofIvy

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

14. Feb 7, 2008

### HallsofIvy

Staff Emeritus
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.