(x+5/x+4)<-1?

Question

Thank You need work

Answer 1

(x+5/x+4)<-1?

(x+5)/(x+4)<-1

Multiply by x+4 on both sides

x+5<-x-4
add x on both sides
2x+5<-4
subtract 5 on both sides
2x<-9
divide by 2 on both sides
x<-9/2

Answer 2

Suppose x + 4 < 0, or x < -4. Multiply through by x + 4 to find
x + 5 > -(x + 4), or x + 5 > -x - 4, or 2x > -9, and so x > -9/2. Therefore, -9/2 < x < -4.

Now assume x + 4 > 0 or x > -4. Then x + 5 < -(x + 4), or x + 5 < -x - 4, so 2x < -9, and x < -9/2. But we cannot have x > -4 and x < -9/2, because -9/2 < -4.

We conclude that -9/2 < x < -4.

Answer 3

(x+5)/(x+4) < -1
(x+5)/(x+4) + 1 < 0
(x+5 + x + 4)/(x+4) < 0
(2x+9)/(x+4) < 0
(x+9/2)/(x+4) < 0

Answer: -4.5 < x < -4

Answer 4

do it urself