# Math Help - inequality

1. ## inequality

x+1/3>=4/x

I got the abswer as (3,+infinite) but according to my book the answer is different.

2. ## Re: inequality

If you multiply both sides by x to get rid of the denominator, you need to take into account 2 cases, one where x > 0 (and the inequality will keep the same sign) and one where x < 0 (and the inequality will reverse its sign).

3. ## Re: inequality

It doesn't.It has 2 roots.

4. ## Re: inequality

Originally Posted by kastamonu
x+1/3>=4/x

I got the abswer as (3,+infinite) but according to my book the answer is different.
You can be pretty sure anything Prove It tells you is correct.

$x + \dfrac 1 3 \geq \dfrac 4 x$

if $x>0$ then

$x^2+\dfrac x 3 - 4 \geq 0$

but if $x<0$ then

$x^2+\dfrac x 3 -4 \leq 0$

you can go ahead and solve these under the 2 conditions

5. ## Re: inequality

first one is (-inf.,-5/3) u (2/3,+inf.)
In the question it is asking how many natural numbers are there that satisfy this equation? By this solution it seems to be infinite.