SOLUTION: I need help solving rational inequalities. I have to solve 4x/x+1 < -3x/x-6 algebraically using a number line and test points. I have to determine when f(x)=4x/x+1 is less than g

Question 109120: I need help solving rational inequalities. I have to solve 4x/x+1 < -3x/x-6 algebraically using a number line and test points. I have to determine when f(x)=4x/x+1 is less than g(x)= -3x/x-6.
I have tried to answer the question but my answer doesn't make any sense to me because I can't tell when f(x) is less than g(x) from when I solved the inequalitie algebraically using the method my teacher taught me.
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
solve 4x/x+1 < -3x/x-6 algebraically using a number line and test points.
--------------------
1st: Determine the values x cannot take.
x=0 because the two fractions would be equal
x=-1 and x=6 because the denominators cannot be zero.
---------------
2nd: Draw a number line and mark x=-1, x=0, and x=6
---------
3rd: Pick a test point from each of the four intervals defined by these x values. Substitute the test value in 4x/x+1 < -3x/x-6 to see if it is true
or false.
In (-inf,-1), pick x=-2, (4*-2)/(-2+1)<(-3*-2)/(-2-6) , false
-------
In (-1,0), pick x=-1/2, (-2)/(1/2))<(-3/2)/(-13/2), true
________
In (0,6), pick x=1. (4/2)<(-3/-5), false
----------
In (6,inf), pick x=7, (28)/(8)<-21/1, false
------------
Solution: -1 ==========================
Cheers,
Stan H.
RELATED QUESTIONS
I need to solve the following inequalities and show on a real number line.... (answered by bucky)

Hello, I desperately need help solving this equation (worked out steps and solution, I (answered by richwmiller)

I need a little help on my homework. I tried them all and I know some of them are right i (answered by greenestamps,jim_thompson5910,ikleyn)

Hi, I'm currently studying solving quadratic inequalities, and I'm having a bit of... (answered by Fermat)

I need some help with these graph problems. I would appreciate some help with solving... (answered by jim_thompson5910)

i need help with the following questions PLEASE!!!! Solve using the multiplication... (answered by solver91311)

I need help solving this rational inequality algebraically. 4/x+2 >... (answered by josgarithmetic,Edwin McCravy)

compound inequalities I really need someone to work this one out with all the steps so I (answered by solver91311)

hey i need help solving this rational equation. Here it is: 1/x - 1/6 = 4/3x^2... (answered by ankor@dixie-net.com)