Question 1172851
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Using a number line may help visualize what's going on.


Graph y ≤ -4 by plotting a closed circle at -4 on the number line and then shade to the left. This indicates "y is -4 or smaller". 


To graph y < -3, we will plot an open circle at -3 and shade to the left. The open circle says "do not include this value as part of the solution set". 


Since we're combining those inequalities with the "or" keyword, this means we're looking for y values that are in either region. 
So either we're in region A which has y = -4 or smaller OR we're in region B which describes y values smaller than -3. 


We can simplify those two regions to combine them to simply region B. 
As the diagram shows, if you are in region A (red), you're already in region B (blue), but not the other way around
<img width="50%" src = "https://i.imgur.com/RzfTOLs.png">


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Now for the next example:
k > 1 and k > 5


To graph k > 1, we have an open hole at 1 and shading to the right to describe all values larger than 1. The value 1 is not part of the solution set.


The graph of k > 5 is similar, but the open hole is at 5 this time.


The keyword here is "and" this time. This means we need to be in BOTH regions at the same time. So we'll look where they overlap. The two regions overlap beyond 5. So that's why "k > 1 and k > 5" simplifies to "k > 5". 


If you pick a number that's both larger than 1 AND larger than 5, then that number is larger than 5. This is because 5 is larger than 1.
<img width="50%" src = "https://i.imgur.com/TGVeFvD.png">


Hopefully these visual diagrams clear your question up. If not, then please let me know. 
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