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

  • Thread starter Thread starter shoook
  • Start date Start date
  • Tags Tags
    Fraction Function
AI Thread Summary
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.
shoook
Messages
23
Reaction score
0

Homework Statement



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



Homework Equations





The Attempt at a Solution



Don't know where to even start.
 
Physics news on Phys.org
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.
 

Thread 'Family of lines that are at a distance of 5 from the origin'

I picked up this problem from the Schaum's series book titled "College Mathematics" by Ayres/Schmidt. It is a solved problem in the book. But what surprised me was that the solution to this problem was given in one line without any explanation. I could, therefore, not understand how the given one-line solution was reached. The one-line solution in the book says: The equation is ##x \cos{\omega} +y \sin{\omega} - 5 = 0##, ##\omega## being the parameter. From my side, the only thing I could...
View full post »

Similar threads

Solve the equation ##x^\frac{17}{6} + x^\frac{21}{25} =15##
Replies
3
Views
2K
Do We Need Boundaries for Fraction Equations?
Replies
21
Views
1K
Solve the given equation that involves fractional indices
Replies
39
Views
3K
Question about fractions
Replies
10
Views
2K
Solve ##x^{\frac{-1}{2}}-2x^{\frac{1}{2}}+x^{\frac{2}{3}}=0##
Replies
24
Views
2K
Find integer points on this equation
Replies
8
Views
1K
Possible values an expression can take : ##\dfrac{x^2-x-6}{x-3}##
Replies
7
Views
1K
Solve the given equation that involves fractional exponent
Replies
4
Views
2K
Prove a rational fraction is equal to another
Replies
5
Views
2K
Find the range of the function ##f(x) = \frac{e^{2x}-e^x+1} {e^{2x}+e^x+1}##
Replies
8
Views
3K

Hot Threads

Recent Insights

Back
Top