How to you tell if an inequality has an open or closed circle? And how would you describe graphs? Example: "open/closed circle on the ______, shading to the _______". :-)

Question

How to you tell if an inequality has an open or closed circle?  And how would you describe graphs?  Example: "open/closed circle on the ______, shading to the _______". :-)

anonymous · Answer

Ok. If it's a ≥ or ≤ sign, then it's a closed circle. If it's a < or > sign, then it's an open circle.
For the shading, you have to plug in a point on one side of the line and see if the solution is true. If it's true, the side of the line that the point was on will be shaded. If it's not shaded, you know that the other side is the one that should be shaded.

anonymous · Answer

so if an equation like 2(x + 5) > 8x – 8
2x + 10 > 8x – 8
10 + 8 > 8x - 2x
18 > 6x
3 > x
x < 3 
would be open and be shaded to the left?

anonymous · Answer

Yes :) Good job! Have you gone over the ones with 2 dimensions as in x and y?

anonymous · Answer

Yes but this is just part of a review lesson and my teacher asked me to explain my graphs and i was unsure how to.  Anyway thanks for showing me!! You helped a lot!! :)

anonymous · Answer

np and glad to help! :)

phi · Answer

the idea is a solid circle includes the "edge value"   x≤3  includes the 3
the open circle is to remind you that you can get close to the value, but not include it
x<3  (very close to 3)