i dont understand interval notation
This is sort of vague, but I’ll do the best I can to explain!
Basically, interval notation is a way to express a set of possible answers. Interval notation is useful especially if you have several difference sets of possible answers with gaps between them. When writing down the answers, it’s important that you list answers from left to right - least to greatest.
For example, if you were asked to write in interval notation the possible answers for x>10 you would write the answer as (10, +∞). Because it asks for only answers GREATER than 10 and because you can never truly reach infinity, you would use parentheses on both ends. Parentheses in interval notation are essentially saying “approaching, but never reaching.” The comma can basically be thought of as an ellipses, denoting all numbers between 10 and infinity.
If you were asked to write the answers for x≥10 you would write the answer as [10, +∞). This time, there’s a bracket on the left and a parentheses on the right. Because the equation asks for answer GREATER than OR EQUAL to, x is allowed to equal 10. A bracket is basically saying that the number immediately following it is also included in the solution set. You would keep the parentheses on the right because you still cannot reach infinity.
Let’s say you’re given something like 10≤x≤15 and were asked to write the solution set in interval notation. That could be interpreted as x is greater than or equal to 10 and less than or equal to 15. You would write the answer as [10, 15]. That is saying that all numbers from 10 to 15 are possible answers.
Interval notation is also used to combine two or more answers sets. Say you were told x≤10 or x>15 and asked to write the answer set in interval notation. The answer would look something like (-∞, 10]U(15, +∞) The answer makes more sense if you plot it on a number line first. Put circles where 10 and 15 are. For the circle on 10, color it in to say that 10 is being included in on the answer set; on 15, leave the circle open so to say that 15 is not included. On the number line, draw a squiggle or color in every number less than 10; now color in every number greater than 15. There’s a gap in the middle; the numbers in this gap are not possible solutions. This means that the answer is in two parts and these two parts are put together with a union sign(U). The first part means that every number approaching negative infinity all the way up to 10 is a possible answer and every answer approaching 15 all the way up to approaching positive infinity is a possible answer.
Hopefully that made at least a little sense!