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

  • Context: Undergrad 
  • Thread starter Thread starter coverband
  • Start date Start date
Click For Summary

Discussion Overview

The discussion revolves around the implications of the inequality 5 < x + 3 < 7 and whether it leads to the conclusion that |x + 3| < 7. Participants explore the relationships between these inequalities and the conditions under which they hold true, touching on concepts of implication in mathematics.

Discussion Character

  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • Some participants argue that 5 < x + 3 < 7 implies |x + 3| < 7, while others contend that the first inequality holding true does not necessarily mean the second must also hold true.
  • One participant notes that |x + 3| < 7 can be rewritten as -7 < x + 3 < 7, leading to the conclusion that -10 < x < 4, while 5 < x + 3 < 7 leads to 2 < x < 4.
  • Another participant expresses confusion regarding the lecturer's explanations, suggesting that the subject matter is difficult to grasp.
  • There is a discussion about the definition of "implies" in mathematical terms, with some participants clarifying that "A implies B" means whenever A is true, B must also be true, but the converse does not necessarily hold.
  • One participant acknowledges a potential misunderstanding due to language barriers, suggesting that their grasp of the implications may be affected by their non-native English proficiency.
  • Another participant points out that while 2 < x < 4 implies -10 < x < 4, the reverse is not true, indicating a lack of biconditionality between the two inequalities.

Areas of Agreement / Disagreement

Participants express differing views on whether 5 < x + 3 < 7 implies |x + 3| < 7, with no consensus reached on the implications of these inequalities. The discussion remains unresolved regarding the nature of the relationship between these statements.

Contextual Notes

Participants highlight potential misunderstandings related to the implications of inequalities and the definitions of mathematical terms, but these remain unresolved within the discussion.

coverband
Messages
170
Reaction score
1
If 5<x+3<7 does this imply |x+3|<7 ??

If 5<x+3<7 does this imply |x+3|<7 ??
 
Mathematics news on Phys.org
coverband said:
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.
 
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
 
"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
 
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| ?
 
coverband said:
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.
 
sutupidmath said:
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.

The linguistic convention in math is that "A implies B' means precisely that there is no case when A holds and B doesn't.
 
sutupidmath said:
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.
?? 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
HallsofIvy said:
?? 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!
 
  • #11
HallsofIvy said:
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
 
  • #12
well if x is greater than two it's certainly greater than 10...
 
  • #13
matticus said:
well if x is greater than two it's certainly greater than 10...
! Oh, wait, that was a typo. "greater than -10".
 
  • #14
coverband said:
But in the first one 2<x<4, in the second one -10<x<4

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.
 

Similar threads

MHB -s6.6 solve exponential eq 3^x-14\cdot 3^{-x}=5
  • · Replies 1 ·
Replies
1
Views
1K
MHB Solving $x^3+y^3=7$ and $x^2+y^2+x+y+xy=4$ System of Equations
  • · Replies 1 ·
Replies
1
Views
1K
MHB How Do You Solve the Absolute Value Equation -3|x+5| + 1 = 7|x+5| + 8?
  • · Replies 3 ·
Replies
3
Views
2K
MHB Evaluate 3/7 r + 5/8 s when r = 14 and s = 8
  • · Replies 3 ·
Replies
3
Views
4K
MHB A=1×3×5×7+3×5×7×9+5×7×9×11+−−−+(2n−3)×(2n−1)×(2n+1)×(2n+3)
  • · Replies 2 ·
Replies
2
Views
2K
MHB Show, that (7+5√2)^(1/3)+(7−5√2)^(1/3) is an integer
  • · Replies 3 ·
Replies
3
Views
1K
MHB 6.6.63 ln(7-x)+ln(1-x)=ln(25-x)
  • · Replies 1 ·
Replies
1
Views
1K
MHB V.02.Binary operator by a*b=a+8b
  • · Replies 2 ·
Replies
2
Views
854
High School A Pi Question: Why do we use the awkward approximation 22/7 ?
  • · Replies 171 ·
6
Replies
171
Views
12K
Undergrad What is the missing number in this number sequence pattern?
  • · Replies 3 ·
Replies
3
Views
4K