Graphing Systems of Linear Inequalities question

[AngelRoman]

I am having trouble with figuring out where to put the 4 red dots on the graph. The red dots will instantly shade the entire part of the graph it is on. I believe if two red dots are on one part of the graph then it's a double shade. But whenever I submit the answer, it's wrong and I think I'm having trouble with knowing where to put those red dots.

 

[lev888]

View attachment 29062
View attachment 29063
I am having trouble with figuring out where to put the 4 red dots on the graph. The red dots will instantly shade the entire part of the graph it is on. I believe if two red dots are on one part of the graph then it's a double shade. But whenever I submit the answer, it's wrong and I think I'm having trouble with knowing where to put those red dots.

Can you post your solution?

 

[AngelRoman]

Yeah, no problem. When you solve the system of inequalities you get this:

Or if you want to see all of the steps:

 

[lev888]

Yeah, no problem. When you solve the system of inequalities you get this: View attachment 29064

Or if you want to see all of the steps:
View attachment 29065 View attachment 29066

1. You have a "simplify" step, but the final inequalities don't look simplified - it's not obvious which line corresponds to which inequality.
2. I understand you have trouble with the red dots. But can you describe (or draw) which region _should_ be the solution?

 

[AngelRoman]

I would say the region on the right side should be double shaded, the bottom should be shaded, and the top should be shaded. The left should be unshaded.

 

[lev888]

I would say the region on the right side should be double shaded, the bottom should be shaded, and the top should be shaded. The left should be unshaded.
View attachment 29067

Looks correct to me. The lines should be solid because these are not strict inequalities? What happens if you put all dots in the right-most region?

 

[AngelRoman]

Yeah, the lines should be solid. Thanks a lot, putting all of the dots on the right side turned out to be correct. May I ask how you knew that all of them belonged on the right side? Again, thanks for your time and help

 

[lev888]

Yeah, the lines should be solid. Thanks a lot, putting all of the dots on the right side turned out to be correct. May I ask how you knew that all of them belonged on the right side? Again, thanks for your time and help

It asked to move the dots so "they all lie within the solution set". That would be the right region.