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Question 78778: how do i graph these conjunctions?
-3 < x and c < 0
-4 < x < -1
Answer by mathdoc314(58)   (Show Source):
You can put this solution on YOUR website! The first question looks weird to me.
You asked: -3 < x and c < 0
You might have meant: -3 < x and x < 0
To graph this you make a number line and color in the numbers that are
between -3 and 0. You make an open circle at the two endpoints -3 and 0
to show they are not included in the set you are graphing. (That is the
set of all numbers that are greater than -3 and less than 0). So it
might look something like this
-5 -4 -3 -2 -1 0 1 2
|---|---O///|///|///O---|---|
I used O for a round circle and //// to show it is shaded.
If you had something different, like -3 <= x and x <= 0, then
the round circle would be filled in solid. But since it is
-3 < x and x < 0 then the endpoints are not shaded so the
circles are left open, unfilled.
There is another interpretation where you meant something more like:
-3 < x and y < 0
where x and y would be two different variables. However 'c' is usually used for a constant, and I am guessing you did not mean to graph this with two different variables.
The second one you do just about the same thing.
It says -4 < x < -1 which means the same as
-4 < x and x < -1 . (Something totally different is
-4 < x OR x < -1, and that disjuction is the same as the
second condition, x < -1,
because it is true whenever the first condition is true.)
I hope that is enough of explanation for you
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