Posted by Tammie on Saturday, July 25, 2009 at 9:45pm.
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
Thank you for the review on this topic!
Related Questions
Pre-Algebra - Can someone please show me how to solve these problems step-by-...
college algebra - Solve the following inequality. x^3+9x^2-108 less or equal to ...
Algebra help - f(x)=x^3-4x^2-x+4 How do I find the x-intercept for this? This is...
Algebra - Solve the linear equation: -10.8x + 1.4 = -47.6 - 1.0x If you could do...
pre algebra - solve the equation step by step.list each step along with the ...
MATH - Look at this inequality 4m-9<2m-3 Solve the inequality for m. ...
calculus--please help!! - Solve the inequality. x^3+9x^2-108 less than or equal ...
Pre-algebra - If zero is known as the trivial solution, what happens when x = 1...
Pre-Algebra [urgent!] - I can't find the solution to this problem; can ...
Algebra 1 - Solve this 5y+4x=4. Can someone please help me solve this step by ...
For Further Reading
