Chapter 2.5, Problem 38E

To determine

(a)

To find:

Whether $x+4$ is positive or negative when $x>-4$.

To determine

(b)

To find:

Whether $x+4$ is positive or negative when $x<-4$.

To determine

(c)

To find:

Whether to change the direction of the inequality sign when we multiply by $x+4$ on both sides of the inequality $\frac{1-x }{x+4}\ge 0$.

To determine

(d)

To explain:

The usage of the parts (a)-(c) to solve the inequality $\frac{1-x }{x+4}\ge 0$ correctly.