SOLUTION: Ugh...here we go again....not in textbook, from teacher and this is driving me nuts. I catch on to some I think but the rest...well gets frustrating.:-( Here's the question:

Question 85112This question is from textbook Blitzer
: Ugh...here we go again....not in textbook, from teacher and this is driving me nuts. I catch on to some I think but the rest...well gets frustrating.:-(
Here's the question:
Solve the rational inequality and graph the solution set on a real number line.
x-6
---- > 0
x+1
Then it just has a straight line graph only going horizonal with 0 through 9 on the right and 0 through -9 on the left. This question is from textbook Blitzer

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Solve the rational inequality and graph the solution set on a real number line.
x-6
---- > 0
x+1
----------
The fraction is >0 when both numerator and denominator are positive
or when both numerator and denominator are negative.
------------
So you determine when the numerator and the denominator are zero:
That occurs when x=6 or when x=-1
-------------
You draw a number line and plot the two values x=-1 and x=6.
You do this because you know those values are not part of the solution.
---------------
Those numbers break the number line into three intervals:
(-inf,-1) , (-1,6), (6,+inf)
------------------------------
Look for solution values in those three intervals by selecting a test value
for each and substituting into (x-6)/(x+1):
Interval (-inf,-1); pick x=-100; you get (-)/(-) which is >0
this whole interval is part of the solution.
-------
Interval (-1,6); pick x=0; you get (-)/(+) which is <0
this whole interval contains no solutions.
-------------
Interval (6,+inf); pick x=100; you get (+)/(+) which is >0
this whole interval is part of the solution
===============
Final graph
Darken the intervals where the solutions lie:
(-inf,-1) OR (6,+inf)
Draw a circle around the points x=-1 and x=6 as they are NOT
part of the solution.
=================
Cheers,
Stan H.

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