Answer:
Last one.
Step-by-step explanation:
Let's look at the fist one
x+1<-1 and x+1<1
Subtract one on both sides for both inequalities:
x<-2 and x<0
Graph it!
*********************************o x<0
*************o x<-2
________(-2)_________(0)____________
So the inequalities do have some common sets of numbers shared so there is a solution and it is any number less than -2.
Let's look at the second one
x+1<=1 and x+1>=1
Subtract one on both sides for both inequalities:
x<=0 and x>=0
Graph it!
@***************** x>=0
*********************@ x<=0
-----------------------(0)-------------------
The only number included by both graphs is 0 so it still has a solution. The solution is 0.
Let's look at the third one:
x+1<1 and x+1>1
Subtract one on both sides for both inequalities:
x<0 and x>0
Graph it!
************************O x<0
O************************* x>0
---------------------------(0)------------------------------
These inequalities have no overlap. They don't even both include zero because of the open circle (the lack of equal sign). This is the compound inequality that has no solution.
