# How to write answer in interval notation

How to Express Your Answer in Interval Notation By Karl Wallulis; Updated April 24, Interval notation is a simplified form of writing the solution to an inequality or system of inequalities, using the bracket and parenthesis symbols in lieu of the inequality symbols.

Compound inequalities Video transcript Let's do some compound inequality problems, and these are just inequality problems that have more than one set of constraints. You're going to see what I'm talking about in a second.

So the first problem I have is negative 5 is less than or equal to x minus 4, which is also less than or equal to So we have two sets of constraints on the set of x's that satisfy these equations. So we could rewrite this compound inequality as negative 5 has to be less than or equal to x minus 4, and x minus 4 needs to be less than or equal to And then we could solve each of these separately, and then we have to remember this "and" there to think about the solution set because it has to be things that satisfy this equation and this equation.

So let's solve each of them individually. So this one over here, we can add 4 to both sides of the equation. The left-hand side, negative 5 plus 4, is negative 1. Negative 1 is less than or equal to x, right?

These 4's just cancel out here and you're just left with an x on this right-hand side. So the left, this part right here, simplifies to x needs to be greater than or equal to negative 1 or negative 1 is less than or equal to x. So we can also write it like this. X needs to be greater than or equal to negative 1.

I just swapped the sides. Now let's do this other condition here in green. Let's add 4 to both sides of this equation. The left-hand side, we just get an x. And then the right-hand side, we get 13 plus 14, which is So we get x is less than or equal to So our two conditions, x has to be greater than or equal to negative 1 and less than or equal to So we could write this again as a compound inequality if we want.

We can say that the solution set, that x has to be less than or equal to 17 and greater than or equal to negative 1. It has to satisfy both of these conditions. So what would that look like on a number line? So let's put our number line right there.

Let's say that this is You keep going down. Maybe this is 0. I'm obviously skipping a bunch of stuff in between. Then we would have a negative 1 right there, maybe a negative 2.

 Sciencing Video Vault Conceptual basis[ edit ] In this bar chartthe top ends of the brown bars indicate observed means and the red line segments "error bars" represent the confidence intervals around them. Although the error bars are shown as symmetric around the means, that is not always the case. Definition of mark Interval notation Video transcript - [Voiceover] What I hope to do in this video is get familiar with the notion of an interval, and also think about ways that we can show an interval, or interval notation. Algebraic Properties of Equality In interval notation this is: This makes this a 4th degree inequality.

So x is greater than or equal to negative 1, so we would start at negative 1. We're going to circle it in because we have a greater than or equal to. And then x is greater than that, but it has to be less than or equal to So it could be equal to 17 or less than So this right here is a solution set, everything that I've shaded in orange.

And if we wanted to write it in interval notation, it would be x is between negative 1 and 17, and it can also equal negative 1, so we put a bracket, and it can also equal So this is the interval notation for this compound inequality right there. Let's do another one.

Let me get a good problem here.The incremental learning derives its name from the incremental nature of the learning process. In incremental learning, all facets of knowledge receive a regular treatment, and there is a regular inflow of new knowledge that builds upon the past knowledge.

Interval Notation.

This notation is my favorite for intervals. It's just a lot simpler! Let's look at the intervals we did with the set-builder notation: Let's start with the first one: This is what it means; So, we write it like this: Use [or ] for closed dots.

In interval notation this is: (4,) or (, -5) or {-4, 1) If we had not been able to order our factors or if we did not know how to take advantage of factors that can be ordered, this would have been much harder. Here’s a Venn Diagram that shows how the different types of numbers are related.

Note that all types of numbers are considered plombier-nemours.com don’t worry too much about the complex and imaginary numbers; we’ll cover them in the Imaginary (Non-Real) and Complex Numbers section..

Algebraic Properties. Interval Notation. This notation is my favorite for intervals. It's just a lot simpler! Let's look at the intervals we did with the set-builder notation: Let's start with the first one: This is what it means; So, we write it like this: Use [or ] for closed dots. MARK 'MARK' is a 4 letter word starting with M and ending with K Crossword clues for 'MARK'.

Alternate Key Signatures for Transposing Instruments – OF NOTE