Question 23311: I have a question that has two parts. I am at a loss when it comes to Inequalities of this type.
A. x^2 + x > 0
B. x+3/x is < or equal to -2
Thanks
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! This is a bit tricky.
A. Solve x^2+x=0 i.e. the equality .
x(x+1)=0
x = 0 or x= -1
Now, draw a number line and mark -1 and 0 on it.
You now see three segments on the line: one to
the left of -1, one between -1 and 0, and one
to the right of 0.
Now check the inequality for a value in each
of the segments. For example try -10,-1/2,10.
For x=-10, (-10)^2+(-10)>0 ?
100 -10> 0 ?
90 > 0 YES
Therefore the inequality is true for every value
of x<=1.
Do the same for x=-1/2 and for x=10.
You should find the solution is x<-10 or x>10
Cheers,
stan H.
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