What does adding two inequalities represent? Let's say I have two inequalities. Now when I add them, I get a third inequality. Is every solution to this inequality a solution to both the original inequalities, either one of the two or neither?
What does adding two inequalities represent?
 A: I think we can understand it by the following way.
$a>b$ says $a-b>0$.
$c>d$ says $c-d>0$.
Sum of positive numbers is a positive number.
Thus, $a-b+c-d>0$ or $a+c-(b+d)>0$, which says $a+c>b+d$ and we are done!
The second part of your statement is wrong.
For example.
Let $x>3$ and $x>5$.
After summing we get $x>4$ and for $4.5$ we see that $x>5$ is wrong.
A: A solution of a sum of inequalities is a solution of one of the original inequalities. Otherwise we'd have 
$$ a >b $$ 
$$ c > d$$ 
Therefore $ a+c>b+d$, a contradiction. 
This is the only conclusion you can draw. 
A: i am  considering
$$2x+3>1\; \text{and}\; x+1>2$$
these two inequalities represent area not including boundary
and now their sum
$$4x+4>3$$ http://www4f.wolframalpha.com/Calculate/MSP/MSP427821017e477697d9e60000120c365d0dgge811?MSPStoreType=i
I can,t copy the other links so you can understand by reading the graphs that  what each inequality represent............
but each inequality represents different and their sum also....
