Question 1069303: Solve the following inequality. Write the answer using interval notation.
1+2/(x+1)≤2x
Answer by KMST(5328)   (Show Source):
You can put this solution on YOUR website!  <--> 
After that we have to think.
We know that  <-->  is forbidden.
so, either  <-->  ,
or <--> .
We also know that if we multiply both sides of an inequality times a positive number
(or divide by a positive number),
the relationship (greater than, or lesser than) remains the same,
but if we multiply times or divide by a negative number,
the resulting inequality has the opposite sign.
So, for <--> ,
is equivalent to
 <--> <--> <--> ,
and for  <-->  ,
is equivalent to
 <--> <--> <--> .
So, the solutions to will be
the solutions to 
and the solutions to  .
We can factor  ,
which is better than having to find the zeros any other way,
makes it easier to see when when it is positive, negative, or zero.
 for  and for  .
 for  (in between the zeros).
 for  or for  .
The solutions to
are the solutions to  ,
and that is  or  .
The solutions to
are the solutions to  ,
and that is or  .
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