Math Is Fun Forum

thedarktiger

Member

Registered: 2014-01-10

Posts: 91

Inequality stuff :P

For what values of x is (x^2 + x + 3)/(2x^2 + x - 6) >= 0?
I got (-inf, -2) U (1.5, inf) with wolfram alpha, but I want to know how.
Thanks

Last edited by thedarktiger (2014-08-01 00:54:19)

---

Good. You can read.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: Inequality stuff :P

hi thedarktiger

For a question like this, I would start with a sketch of the graph.

(1) The numerator has no real solutions, and is clearly positive when x=0, so it must always be positive.

(2) the denominator will factorise to (2x-3)(x+2), so the graph will have vertical asymptotes at x = -2 and x = 1.5

(3) as x tends to + or - infinity, the function tends to +0.5

(4) At x = 0, function = -0.5

So the graph starts positive; zooms up at x = -2;then takes negative values until x = 1.5; then zooms down from infinity to tend to 0.5 once more.

All that can be deduced without a graph plotter, so I hope you'll forgive me for then using one to get a neat plot.  A hand drawn sketch would serve as well.

It's now easy to answer the question. 

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob