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

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To solve the inequality (x+1)/(x+6) ≥ 0, identify critical points where the numerator and denominator change signs, specifically at x = -1 and x = -6. Analyze the sign of the expression in three intervals: x < -6, -6 < x < -1, and x > -1. In the interval x < -6, the expression is positive; between -6 and -1, it is negative; and for x > -1, it is positive again. Include the endpoints x = -1 and x = -6 since the inequality is non-strict. The solution set is x ≤ -6 or x ≥ -1.
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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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