SOLUTION: Express the inequality as an interval and sketch it's graph. 1. X < -2 I don't understand wat the question is asking or the basic concept? How to do this?

Question 718282: Express the inequality as an interval and sketch it's graph.
1. X < -2
I don't understand wat the question is asking or the basic concept?
How to do this?
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!
An interval is a set of numbers which are between two numbers, a and b. The set may or may not include a and/or b. The notation used for an interval is one of the following:
(a, b)
[a, b]
(a, b]
[a, b)
where "a" is the number at the low end of the interval and "b" is the number at the high end of the interval. A parenthesis, "(") or ")", means that the number at that end of the interval is not included in the set. A bracket, "[" or "]", means that the number at that end of the interval is included in the set.

x < 2 says that x must be less than two. So between which numbers must x be if it less than 2? No matter what low number we pick, like -99999999999, x could still be a lower number. In this case we say the lowest x can be is "negative infinity" which is represented by (Think of the shape as a sideways 8.). So if x < 2 it must be between negative infinity and 2.

Now we just have to ask ourselves do we use a bracket (meaning include the number) or a parenthesis (meaning don't include the number) or negative infinity and for 2. For negative (or positive) infinity, always use parenthesis. Infinity is not a specific number and can never be included in a set of numbers. For the 2, do we want to include 2 in the set? Is it possible for x to be a 2? For x < 2 the answer to this is "no", x cannot be 2. So we will use a parenthesis for 2, too. (If the inequality was then we would use a bracket for the 2.)

This makes the interval: (, 2)

As for the graph, a one variable inequality like x < 2 is graphed on a number line. In theory, we should draw a dot on the number line for every number that is below 2. (The dot means: "including this number") But there's two problems with this:

There are an infinite number of numbers that are below 2. There is no way we can name, much less draw, an infinite number of dots. The way we handle this is to
- Shade (make thicker) the number line to indicate "all the numbers in this part of the number line. (The idea of the shading is that it is an infinite number of dots so close together that we can't see any space between them.)
- If the shading is supposed to go forever in one direction or the other, just put an arrow head, "<" or ">", on that end of the shading. The arrowhead means "and so on forever in this direction".
We do not want a dot (or shading) on 2 because a dot means "include this number" and x cannot be 2 so we do not want to include it. However we do want to include the number just below 2. But what is the number just below 2? The answer: The number just below 2 cannot be named! No matter what number you think it might be it will be possible to name another number that is even closer to 2 (but still less than 2). The way we handle this is to draw a small open circle (or ring) at 2. The open circle is not a dot and it means "not including this number" (just like the parentheses in the interval notation). Then we shade right up to but not over the open circle.

So to graph x < 2:

Draw a number line an label where the 2 is.
Draw a small open circle at the 2.
Shade (make thicker) part of the number line.
1. Start from the open circle and go to the left (where the smaller numbers are).
2. Make the shading be long enough so that it is noticeable.
3. Put a "<" on the left end of the shading to indicate that the shading continues forever in this direction. Note: The number line also has "<" and ">" on each end. The one you put at the end of the shading should be separate from these two.
4. Make sure the open circle does not get filled in by the shading because that would turn it into a dot.

Unfortunately Algebra.com's graphing software does not do graphs of inequalities on a number line so I cannot show you what the graph would look like.

P.S. Please post your problems in an appropriate category. This problem has nothing to do with the category you chose, absolute value. I have changed the category to an appropriate one.
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