Question

How do you solve and graph the compound inequality `3x>=5` or `-5/8x-6>1` ?

Answer 1

It is the union of the two solution sets.

Explanation:

`3x>=5 or −58x−6>1`
`x>=5/3 or 58x<-7`
`x>=5/3 or x<-7/58`
You will have two semi-plane. The "or" operator means that you have to take the union of the two solution set.

graph{x>=5/3 [-10, 10, -5, 5]}

graph{x<-7/58 [-10, 10, -5, 5]}

Answer 2

Solve and graph system
(1) 3x >= 5
(2) -5x/8 - 6 > 1

Explanation:

(1) -> `3x >= 5 --> x >= 5/3`

(2) -> `5x/8 < -7 -> 5x < -56 -> x < -56/5`
Graph:

=========|-56/5 -----------------|0-----|5/3=============

NOTE. The end (critical) point (5/3) is included in the solution set.