Solving Fraction Function Homework: (x+1)/(x+6) >or= 0

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    Fraction Function
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Homework Help Overview

The problem involves solving the inequality (x+1)/(x+6) ≥ 0, which falls under the subject area of algebra, specifically rational functions and inequalities.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants discuss identifying the critical points where the numerator and denominator change signs, with suggestions to analyze the sign of the expression in different intervals.

Discussion Status

The discussion is active, with participants exploring the implications of the critical points x = -1 and x = -6, and considering how to determine the sign of the expression in various intervals.

Contextual Notes

Participants are working within the constraints of the inequality and are encouraged to consider the significance of the endpoints in relation to the inequality sign.

shoook
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Homework Statement



Solve: (x+1)/(x+6) >or= 0



Homework Equations





The Attempt at a Solution



Don't know where to even start.
 
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List all of the x values where the numerator and denominator of the left hand side can change signs. Quick!
 
x=-1 x=-6 ?
 
Great! So if x<-6 what's the sign? If -6<x<-1, what's the sign? If x>-1, what's the sign? You only have three cases. Since it's >or=, you should think about x=-1 and -6 as well.
 

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