SOLUTION: <Could someone please help me to understand how to solve this type of problem? I just cannot seem to get it. I posted another one that is different. Solve each rational inequality

Question 40620: Solve each rational inequality and state the solution set using interval notation.
x + 3/x lessthan or eqaul to -2

(I don't know why this dosen't post right. x + 3 over x is lessthen or eqaul to -2)
Answer by junior403(76) (Show Source): You can put this solution on YOUR website!
Solve the rational inequality and state the solution set using interval notation.

Ok, first we need to eliminate the fraction by multiplying both sides of the equation by the denominator x.
This will create an equation that we can work with more easily.

Now we can simplify by canceling out the x's on the left side and multiplying on the right.

Now we can subtract the x from both sides of the equation...
x + 3 - x = 3 and -2x -x = -3x
so...

Now, this may get a little tricky...
We need to isolate the variable x. In order to do that we need to divide both sides by -3.
However, the rule for inequalities is that when we divide by a NEGATIVE number, we ALWAYS have to chanbge the inequality sign. so...
3/-3 = -1 and 3x/3 = x
And remember to change the sign.
So...

So this tells us that our variable x will always be less than or equal to -1.
The bracket ] tells us that -1 is included.
So we show this in interval notation...
(-~,-1] or (negative infinity, -1]
I hope this helps.
Good Luck!

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