HI debjit625

Sorry, I just misunderstood what you were saying about + / - 4

What you have just said is correct, no problem.

In post 1 you had two ranges, in words below -5 and above + 5

Those are both correct and my graph shows these.

What was missing from your answer was another range of possible values for x, between -3 and + 3

Look at my graph and you can see that, in this range, 'y' is always negative, so certainly < 1/2

So why did these values 'go missing' ?

The graph has a discontinuity at -3 and again at +3 because of the division by zero.

So you need to check in this range too.

I tried to demonstrate why (-3,0) is another set of values that fit the inequality. Twice I had to use the rule that **'if you multiply or divide by a negative, you must reverse the inequality'**. Do you know and understand this rule?

I have recently posted an explanation at

[url]http://www.mathisfunforum.com/viewtopic.php?id=18411[/math]

You might like to have a look at that, especially post 7 in that thread.

I've got to log off for a short while. I'll be back on in about 15 mins.

ADDITIONAL EDIT:

case 3 which you actually explained in post #5 gives

but as already given

If I call

... statement one and

... statement two, then we can work the logic like this.

I got statement one by algebra assuming statement two. So statement one is only true to the extent that it obeys statement two. As statement two is a subset of statement one that means the inequality is satisfied just for the subset ie

So that provides part of the missing answer.

Testing x = 0 by substitution shows it may be added to the set giving

You can finish by considering (0,+3) and showing it is legitimate to add this to the range

Bob