Saturday

December 20, 2014

December 20, 2014

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

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 10:10pmThere 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 10:28pmThank you for the review on this topic!

**Answer this Question**

**Related Questions**

Algebra - Solve the inequality: x+8 over x-1 > OR = 0 Write the solution set ...

college algebra - Solve the following inequality. x^3+9x^2-108 less or equal to ...

Solve Inequality - Solve the inequality. Express your solution using interval ...

math - solve the polynomial inequality and graph the solution set on a real ...

algebra - solve the inequality and write the solution set using interval ...

math - can some one solve this Ex 1: -2x+7>22 -2x+7-7>22-7 -2x>15 -2x...

calculus--please help!! - Solve the inequality. x^3+9x^2-108 less than or equal ...

Algebra - Solve and express in interval notation Solve: |5 8x| > 11 and ...

math-please help,need quickly - solve the polynomial inequality and graph the ...

calculus - solve the following inequality. write your solution in interval ...