Algebra (all content)
Plotting an inequality example
Learn how to plot a simple inequality on a number line. The example used in this video is x < 4. Created by Sal Khan and Monterey Institute for Technology and Education.
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- Hello! Can anyone help me? How do you remember the difference between: ≤ ≥ < > and the open dot and the closed dot. Also, for example, if there's the problem: x ≤ 5 . Here's my questions (P.S.: This all applies to a number line): Which direction should the line go? Should the dot be opened or closed? Is there a way to remember it? Thanks to y'all for answering! Plz try and answer soon! Bye!(15 votes)
- Not sure if you know the signs or not, but one way of thinking about greater than and less than is to make signs with your thumb and pointing finger. If the sign looks like your left hand (<), left is less than. If the sign looks like your right hand (>), Tony the Tiger says right is Grrrrrrrrrrrreater. If you have a line underneath (≥ or ≤) you have to add the phrase or equal to, so ≥ is greater than or eqaul to and ≤ is less than or equal to.
As far as the open and closed circle, the best way is to understand what it really means. If you were just going to show x=3, you would put a closed dot on 3. So a closed dot means the point counts and you need the equal sign below the line (≥ or ≤). If you have an open circle, the point does not count, thus no equal line. If you have a positive variable on the left, the sign points toward the direction that you draw the line (so x< and x≤ both point toward the left, so start at your point (either open or closed), draw left and end with an arrow <------. If the sign points to the right (> or ≥), then start at point (either open or closed) and draw to the right --------->.
Does this help, or do you need more?(9 votes)
- when do you close the circle?1!(12 votes)
- graph x is less than 4.0 lets draw yourself a number line(7 votes)
- what does it mean when the dot is open on the 2 and the line is going both negative and positive ways?(12 votes)
- It means that All Real Numbers except 2 is the solution.(6 votes)
- For some reason, I cannot remember when to use an open circle, and when to use a solid dot on these number lines.(6 votes)
- I always remember: an open circle is around the number, so it doesn't actually touch the number, meaning it does not include the number itself. A filled in dot is really on the number itself, so that does include the number.(13 votes)
- I Love Math WOOWOO! GO MATH!(7 votes)
- Good for you if you love math so much than ask a math question or make a math statement.(0 votes)
- How would you graph x=4?(5 votes)
- Vertical line going through 4 on x axis.(3 votes)
- How i can solve this:
16< |6-3x| < 19 ?(4 votes)
- Split it into a compound inequality:
16< |6-3x| and |6-3x| < 19
Solve each individually, then find the intersection of the two results.(4 votes)
- Would it still be x < 4 if you did not put a circle on 4?(3 votes)
- The dot or circle is always used so there is no ambiguity as to where the inequality starts. An open dot tells you that the inequality is "<" or ">" with the arrow's direction telling you which applies. A solid dot tells you that the inequality is ">=" or "<=".(5 votes)
- Is 6/8 greater than 6/10(2 votes)
- Yes. To double check, you can convert
6 / 8to
30 / 40and
6 / 10to
24 / 40.
6 / 8 = 30 / 40is greater than
6 / 10 = 24 / 40.(7 votes)
Graph x is less than 4. So let's draw ourselves a number line over here. So let me draw a number line. I'll start here at 0, so 0, 1, 2, 3, 4, 5. And we could go below 0. We'd have negative 1, negative 2, negative 3, negative 4. I could keep going. Now, we want to graph all of the x's that are less than 4, but we're not including 4. It's not less than or equal to 4. It's just less than 4. And to show that we're not going to include 4, what we're going to do is we're going to draw a circle around 4. So this shows us that we're not including 4. If we were including 4, I would make that a solid dot. And to show that we're going to do all the values less than 4, we want to shade in the number line below 4, going down from 4, just like that. And then we can just shade in the arrow just like that. So this right here is all of the values less than 4. And you could test it out. Take any value where there's blue. So there's blue over here, negative 2. Negative 2 is definitely less than 4. If you take this value right here, this 2, it's definitely less than 4. 4 is not included because 4 is not less than 4. It's equal to 4. 5 is not included because 5 is not less than 4.