William W. answered • 01/18/20
Top Algebra Tutor
Rational inequalities are tricky. To me the easiest way to solve them is to make them into an equality which will find the intersection point of the two sides of the equation (it finds what x-values make (7-x)/(x+1) equal to (4-x)/(x+3). Those points will be the boundaries of the inequality. Additionally, we need to include evaluating what happens around the asymptotes so we will include those.
So let (7-x)/(x+1) = (4-x)/(x+3). Cross multiply to get:
(7 - x)(x + 3) = (x + 1)(4 - x)
-x2 + 4x + 21 = -x2 + 3x + 4
4x + 21 = 3x + 4
x = -17
So x = -17 is a boundary.
The asymptotes are x = -3 and x = -1 so we will include those as possible boundaries
Next, we draw a number line which includes the boundaries we have found.
Then we try out numbers in each of the boundary-divided segments.
This tell us that the answer is:
-17 < x < -3 and x > -1
William W.
You are absolutely right. Let's try it again. I modified my answer.01/20/20
Dewie B.
Something about your answer isn't right. I tried x= -2 and the inequality came out false.01/20/20