Question

How do you graph the inequality `1<x<3`?

Answer 1

                o---------o
<-|-----|-----|-----|-----|-----|-----|->
  -1----0----1----2----3----4----5

Explanation:

Ok so please excuse the answer in the graph, it's very messy because Socratic doesn't yet have a number line feature.

So first, we know we have to use a number line because only one variable is used (x).

Now, I'm going to write it out in words.
One is less than x, which is less than Three

Since the two bounds, or the numbers on the outside, are 1 and 3, I think a reasonable place to start and end the number line are -1 and 5. So, I drew a line and labeled the following points on it: `[-1,0,1,2,3,4,5]`

Make sure to have them evenly apart.
Ok, so now let's talk about actually graphing it. Let's start with the lower bound, 1.''

Since one is less than x, we know that we should draw an open circle above one. If one was less than or equal to x, we would color in the circle. Since it is not equal to x, we leave it not colored in.

Next let's move on to the upper bound, 3. Since x is less than three, we would draw a circle above 3. We won't color it in because it's not equal to 3.

Finally, since X is inbetween 1 and 3, we draw a line between them.
And there you have it.

To recap:

• Draw the number line including the two bounds
• Make a point at the lower bound. Color it in if that bound is less than or equal to x.
• Make a point at the upper bound. Color it in if x is less than or equal to that bound.

Cheers!