SOLUTION: Solve the following inequality. Write the answer using interval notation.
1+2/(x+1)≤2x
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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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