How to find counterexample in these statements?

[butterscotchplz]

1. For all numbers x, x> 1/x

2. For all numbers x, x+x>x

3. For all numbers x, x^3 ≥ x

4. For all numbers x, |x+3|=|x|+3

5. For all numbers x, -x<x

 

[Deleted member 4993]

1. For all numbers x, x> 1/x

2. For all numbers x, x+x>x

3. For all numbers x, x^3 ≥ x

4. For all numbers x, |x+3|=|x|+3

5. For all numbers x, -x<x

Please show us what you have tried and exactly where you are stuck.

Please follow the rules of posting in this forum, as enunciated at:

https://www.freemathhelp.com/forum/threads/read-before-posting.109846/#post-486520​

Please share your work/thoughts about this problem.

 

[Dr.Peterson]

How to find counterexample in these statements?

1. For all numbers x, x> 1/x
2. For all numbers x, x+x>x
3. For all numbers x, x^3 ≥ x
4. For all numbers x, |x+3|=|x|+3
5. For all numbers x, -x<x

If the first couple examples you try work (not counterexamples), then try some more unusual cases - negative numbers, fractions, 0, things like that.

Or, you might try graphing the two sides and see when they don't have the required relationship.

 

[pka]

1. For all numbers x, x> 1/x_____________________2. For all numbers x, x+x>x

3. For all numbers x, x^3 ≥ x_____________________4. For all numbers x, |x+3|=|x|+3

5. For all numbers x, -x<x

In no particular order: \(x=-2,~~x=\frac{1}{2},~~x=-1\) are counter-examples for at least one these.
You tell us which goes to which and why.

 

[Erinn]

Please show us what you have tried and exactly where you are stuck.

Please follow the rules of posting in this forum, as enunciated at:

https://www.freemathhelp.com/forum/threads/read-before-posting.109846/#post-486520​

Please share your work/thoughts about this problem.

1 and 2

 

[Erinn]

1. For all numbers x, x> 1/x

2. For all numbers x, x+x>x

3. For all numbers x, x^3 ≥ x

4. For all numbers x, |x+3|=|x|+3

5. For all numbers x, -x<x

Can you help me on 1 and 2?

 

[Deleted member 4993]

Can you help me on 1 and 2?

Yes ... we can. But first you have to let us know "what do you understand" and why you are having trouble with 1 and 2 - by showing "your work" on these problems.

 

[Steven G]

For these type problems I like to think that there are 3 different types of positive numbers (and three types of negative numbers)
Think
1) 0<x<1
2) x=1
3) x>1
I mainly included number 2 for completeness.