Inequalties problem

[alearon]

Problem in solving an inequality?
2/(x+1) <= 3

I can derive from this that x =/ -1 as that would cause the LHS to be undefined.
I can also derive from this that -1/3 <= x

When working this out however, I get the following error:
2/(x+1) <= 3
2<= 3(x+1) if (x+1) is +
as well as 2>= 3(x+1) if (x+1) is -

This then means that as well as getting -1/3 <= x as a solution, I also get -1/3 >= x as a solution.
I know that the answer is -1 >= x and -1/3 <= x. Can anyone tell me what I have done wrong? Please help!
Thankyou

 

[mmm4444bot]

2 >= 3(x+1) if (x+1) is -

This then means that … I also get -1/3 >= x as a solution.

Not quite. You're forgetting to take the intersection of two inequalities, in the case above.

When you state the case that x + 1 is negative, you're implicitly saying that x < -1.

You then solved under this assumption and found that x < -1/3.

So, you have two conditions that must be true simultaneously.

x < -1 AND x < -1/3.

Take the intersection of these two sets.

 

[alearon]

Thank you!