Is this right method?

[Shooter]

1/5 < 1/(x+1) < 1/2

Can I write this inequality as this?

1/(5-1)<1/(x+1-1)<1/(2-1)

=> 1/4<1/x<1/1
=> 4>x>1

=> 1<x<4

Hence the values 'x' might be '2' and '3'.

Thanks for your help.

[Makumajon]

Here it works, not because of the possibility of -1 in the first step but because of the inversion in the third step.

1/5 < 1/(x+1) < 1/2. Well, you see if you can invert 1/(x+1), you can easily solve it. But before inverting inequality, you must check all parts of the inequality to ensure that none can be negative. Here 1/5, 1/2 cannot be negative. So, 1/(x+1) also cannot be. Hence, you can safely invert the inequality by reversing the sign:

5>(x+1)>2. If you find a variable portion can be negative or positive, you must stop inverting.

[Shooter]

Thanks a lot buddy.

[bose]

thanks makumajon

[rishanthchavali]

thanx a lot..................