Posted by **Tammie** on Saturday, July 25, 2009 at 9:45pm.

Just wondering if I did this correctly step by step. If not corrections are mostly appreciated!

Solve the inequality and write the solution set in interval notation. Show work/explanation.

(x+8)/(x-1) >= 0

8+x/x-1=1+9/x-1

9/x-1>=-1

x-1/9 < -1

x-1< -9

x<-8

x-1>0

x>1

x+8/x> = 1

x^2+8> = x

8 > -1

x-1/9<=-1

x-1<=-9

x<=-8

x-1>0

x>1

Final Answer:

x < -8 OR x>1

(-,-8] (1, )

Is this all of what I need to show for how I got my answer?

- Algebra -
**Reiny**, Saturday, July 25, 2009 at 10:10pm
There are several ways to do this.

Your way is the oddest way I have ever seen. It looks like you are actually doing a long division to get

(8+x)/(x-1)=1+9/(x-1) (notice my brackets to make your statement from above actually true.)

Here is a logical way:

since the answer to the fraction is positive, either both top and bottom are positive or they are both negative.

That is,

[x+8≥0 and x-1>0] OR [x+8≤0 and x-1≤0]

[x≥-8 and x>1] OR [x≤-8 and x≤1]

x > 1 or x ≤ -8

so you did get the right answer.

The way I do these is this :

From the factored form, I can see two "critical values" namely -8 and 1

So my number line is split into 3 sections:

a) x ≤ -8

b) between -8 and 1

c) x >1

I then pick an arbitrary number in each region. We don't actually have to evaluate, just get the sign correctly.

a) let x=-10, then -/- >0 , which works

b) let x=0, then +/- < 0 , does not work

c) let x=10 then +/+ > 0 , works

so x ≤ -8 or x > 1

- Algebra -
**Tammie**, Saturday, July 25, 2009 at 10:28pm
Thank you for the review on this topic!

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