#1**+1 **

Multiply both sides by z+1 to get

(BUT there is another consideration.....see Geno's answer below)

ElectricPavlov Mar 18, 2020

edited by
ElectricPavlov
Mar 18, 2020

edited by ElectricPavlov Mar 18, 2020

edited by ElectricPavlov Mar 18, 2020

edited by ElectricPavlov Mar 18, 2020

edited by ElectricPavlov Mar 18, 2020

#2**0 **

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.

geno3141 Mar 18, 2020