+36915 Multiply both sides by z+1 to get
(BUT there is another consideration.....see Geno's answer below)
+23246 To solve (3 - z) / (z + 1) >= 1
you need to consider two situations:
1) when z + 1 is positive, and
2) when z + 1 is negative.
For situation 1: z + 1 > 0 ---> z > -1
Solving by multiplying both sides by z + 1 ---> 3 - z >= z + 1 ---> 2 >= 2z ---> z <= 1
But, we must combine that with the restriction that z > -1 to get: -1 < z <= 1
Now, for the situation when z + 1 is negative ---> z + 1 < 0 ---> z < -1
Multiplying both sides by z + 1 (since z + 1 is negative, we must change the direction of the inequality)
---> 3 -z <= z + 1 ---> 2 <= 2z ---> 1 <= z ---> z >= 1 This is impossible, so we must reject this possibility!
We have to consider both possibilities because we have to change the direction of the inequality.
