Simplifying Expressions

[johnny101]

This is a review problem from the text and I really don't understand how to go about this. Note: Like the earlier post I have all the problems have not enough information as an option. Can someone explain this problem?

Simplify:

If a <= b

(a+b/2) + (|a-b|/2).

Help!

 

[stapel]

Can someone explain this problem?

Simplify: If a <= b

(a+b/2) + (|a-b|/2)

The only point I see to the restriction "a < b" is to allow you to remove the absolute-value bars correctly. Otherwise, this is just a straightforward algebraic manipulation. :wink:

 

[johnny101]

The only point I see to the restriction "a < b" is to allow you to remove the absolute-value bars correctly. Otherwise, this is just a straightforward algebraic manipulation. :wink:

Meaning there isn't enough information here to solve this?

 

[stapel]

Meaning there isn't enough information here to solve this?

No; "this is just a straightforward algebraic manipulation" means that this is a simple issue of doing some algebra to rearrange things. The point of the restriction is to allow the rearrangement to take place.

 

[johnny101]

How can we manipulate that without any integers though or data? I'm confused >.>

 

[pka]

How can we manipulate that without any integers though or data? I'm confused >.>

If \(\displaystyle a\le b\) then \(\displaystyle |a-b|=-(a-b)=b-a\)

 

[johnny101]

if we have the division shouldn't we try to get rid of the denominator so multiply them out, i mean if we just subtract then we come up with 0...no?

 

[pka]

if we have the division shouldn't we try to get rid of the denominator so multiply them out, i mean if we just subtract then we come up with 0...no?

Look if \(\displaystyle a\le b\) then
\(\displaystyle \dfrac{{a + b}}{2} + \dfrac{{\left| {a - b} \right|}}{2} = \dfrac{{a + b}}{2} - \dfrac{{a - b}}{2} = b\).

That is a classic programming trick to pick the larger of two numbers.

 

[johnny101]

wow ok thank you i was off base