Question

How do you solve and graph `-y+5>=9` or `3y+4< -5`?

Answer 1

See below

Explanation:

First rearrange the inequalities so y is the subject:

`-y+5>=9color(white)(88)` , `color(white)(88)-y >=4` , `color(white)(88)y<=-4`

`3y+4<-5` , `color(white)(88)3y<-9` , `color(white)(88)y<-3`

`color(blue)(y<=-4)`

`color(blue)(y<-3)`

Graph these two lines as `y=-4` and `y=-3`. Remember to use a dashed line for `y=-3`, because this is a less than and not a less than or equal to inequality, so the line will not be an included region.

We now need to test `y` values in each region A , B and C. These values have to satisfy both inequalities:

Region A:

`y=-1`

`-1<=-4color(white)(88)` False

`-1<-3color(white)(88)` False

A is not an included region.

Region B:

`y=-3.5`

`-3.5<=-4color(white)(88)`False

`-3.5<-3color(white)(8)` True

Region B is not the included region.

Region C:

`y=-5`

`-5<=-4color(white)(88)`True

`-5<-3color(white)(88)`True

Region C satisfies both, so region C is the included region.