Re: Solving inequality

On Mar 4, 3:07 pm, Passerby <inva...@xxxxxxxxxxxxxxx> wrote:
On 3 Mar 2007 20:07:40 -0800, "MQ" <michaelquinli...@xxxxxxxxx> wrote:

Hi there, I'm trying to solve the inequality (5x - 2)/(x(x-1)) < 6. I
think I have found the right answer, but since I made this problem up
for myself, I cannot check if it is right (ie not a textbook
question). Can anyone confirn that I indeed have the correct answer?
I have tried subbing some values and it seems to work. Thanks in
advance.

[snip]

(x - a)(x - b) < 0 (where a is [11+sqrt(73)]/12 and b is [11-sqrt(73)]/
12)
This is valid when (x-a)<0 AND (x-b)>0, or x<a AND x>b, or (b,a) since
b<a
It is also valid when (x-a)>0 AND (x-b)<0, or x>a AND x<b. No
solution here since b<a
So, solution is (b,a), but since we assumed that x = (0,1), finding
the intersection we get x = (b,1)

Combining the two solutions together from both cases, we get x = (-oo,
0] U (b,1) U (a,oo)

Don't think the solution includes x = 0, agree otherwise.

x < 0

1/12 ( 11 - sqrt(73) ) < x < 1

x > 1/12 ( 11 + sqrt(73) )

Ah, yes of course, missed that one, the denominator of the expression
is zero when x=0, so is undefined

.

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