- #1

coverband

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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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- Thread starter coverband
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In summary, the conversation discusses the implications of the inequality 5<x+3<7 on the inequality |x+3|<7, as well as the bounds for |x+3| in different equations. It also addresses the linguistic convention in math regarding the use of "implies" and its converse. The conversation also includes a clarification on a typo in the first inequality mentioned.

- #1

coverband

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

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- #2

sutupidmath

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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?

- #3

sutupidmath

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- #4

coverband

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- #5

coverband

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Thanks i think

- #6

coverband

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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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coverband said:

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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DeadWolfe

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sutupidmath said:

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

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.sutupidmath said:

- #10

sutupidmath

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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

coverband

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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

matticus

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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".matticus said:well if x is greater than two it's certainly greater than 10...

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HallsofIvy

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

That's why it is

The inequality 5

We can prove this by using the properties of absolute value and the given inequality. Since 5

Yes, the two inequalities are equivalent. They both represent the same range of values for x+3, which is between 5 and 7. The only difference is that the absolute value inequality explicitly states that the distance of x+3 from 0 is less than 7.

No, if |x+3| is greater than or equal to 7, then the inequality 5

This concept can be applied in various real-life scenarios, such as measuring the accuracy of a scientific experiment or calculating the probability of an event occurring within a certain range. For example, if an experiment has an expected result between 5 and 7, then any result with an absolute value less than 7 would be considered accurate.

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