# Rational inequality

• Oct 28th 2007, 08:45 PM
soly_sol
Rational inequality

Solve the rational inequality and graph the solution set on a real number line. Express the solution set in interval notation.

7. (x-5)/(x+2)>0
this is what I got:

x-5=0 or x+2=0
(I added 5) (I subtracted 2)

got: 5>0 or -2>0

graph (-∞, -2) or (5, ∞)
http://i48.photobucket.com/albums/f2...sol/f1q7g6.jpg

8. (-x+8)/(x-3) > or equal to 0
this is what I got:

-x+8 = 0 x-3=0
(I subtracted 8, then divided by -1) (I added 3)

I then got x=8 x=3

graph: (3, 8]
http://i48.photobucket.com/albums/f2...sol/f1q8g3.jpg

9. (2)/(x-2) < 1 (I wasnt too sure how to do this one)
graph: (2, 4)
http://i48.photobucket.com/albums/f2...sol/f1q9g3.jpg

10. (10-2x)/(4x+5)< or equal to
this is what I got:

10x-2x=0
I subtracted 10, then divided by -2x and x=5

4x+5=0
I subtracted 5, then divided by 4x, and x= -5/4

graph: (-∞, -5/4) or [5, ∞)
http://i48.photobucket.com/albums/f2...ol/f1q10g9.jpg
• Oct 28th 2007, 09:39 PM
CaptainBlack
Quote:

Originally Posted by soly_sol

Solve the rational inequality and graph the solution set on a real number line. Express the solution set in interval notation.

7. (x-5)/(x+2)>0
this is what I got:

x-5=0 or x+2=0
(I added 5) (I subtracted 2)

got: 5>0 or -2>0

graph (-∞, -2) or (5, ∞)
http://i48.photobucket.com/albums/f2...sol/f1q7g6.jpg

Your given answer does not agree with the diagram. You should have

x>5 or x<-2

RonL
• Oct 28th 2007, 09:43 PM
CaptainBlack
Quote:

Originally Posted by soly_sol
8. (-x+8)/(x-3) > or equal to 0
this is what I got:

-x+8 = 0 x-3=0
(I subtracted 8, then divided by -1) (I added 3)

I then got x=8 x=3

graph: (3, 8]
http://i48.photobucket.com/albums/f2...sol/f1q8g3.jpg

The equality holds when x=8, and the expression changes sign also at x=3
also at x=5 the expression is positive so the inequality holds when:

x<=8, and x>3, which is the interval (3,8].

RonL