How to find the relation among some forumals

[robroc]

We know that a < 4b

I need to find the relation of (greater than, less than, etc)

a - b to (a/2) + b
and a - b to (a/2)


Could you please help?

Thank you in advance

 

[tkhunny]

Have you tried building the structures?

If a < 4b, then a-b < 3b, a/2 < 2b, and a/2 + b < 3b. It might lead to something.

 

[robroc]

Have you tried building the structures?

If a < 4b, then a-b < 3b, a/2 < 2b, and a/2 + b < 3b. It might lead to something.

Thank you for the reply.
In this case how do relations

a/2 + b and a-b relate since they are both < 3b?


Thanks again

 

[pka]

In this case how do relations
a/2 + b and a-b relate since they are both < 3b?

The average of two numbers is between them.
\(\displaystyle a<\dfrac{a+4b}{2}<4b\)

\(\displaystyle a<\frac{a}{2}+2b<4b\)

\(\displaystyle a-b<\frac{a}{2}+b<3b\)

 

[robroc]

The average of two numbers is between them.
\(\displaystyle a<\dfrac{a+4b}{2}<4b\)

\(\displaystyle a<\frac{a}{2}+2b<4b\)

\(\displaystyle a-b<\frac{a}{2}+b<3b\)

Thank you so much!