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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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  • blobby green style avatar for user Amber Alexis Pantle
    How do you solve an inequality if there is a value that is squared such as 2x^2 +2x< 12?
    (27 votes)
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    • old spice man green style avatar for user Dan Surerus
      you would have to factor it.
      2x^2+2x-12<0 ; divide both sides by 2

      x^2+x-6<0
      (x+3)(x-2)<0
      (x+3)<0 OR (x-2)<0
      x<-3 OR x<2

      so x is less than negative 3 or x is less than 2. You can just say x is less than 2 for the overall answer.

      Answer: x<2

      You can see if you put 2 into the equation you get 12<12 so x must be less than 2, It can be 1.9999999 forever and anything less than that, but not 2 or above.
      (20 votes)
  • aqualine tree style avatar for user flawabud101
    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!
    (14 votes)
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    • mr pink green style avatar for user David Severin
      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?
      (10 votes)
  • mr pink red style avatar for user Walker, Lauren
    when do you close the circle?1!
    (13 votes)
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  • blobby green style avatar for user Gina Marquez
    what does it mean when the dot is open on the 2 and the line is going both negative and positive ways?
    (13 votes)
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  • leafers ultimate style avatar for user Val B.
    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)
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    • leafers seedling style avatar for user Britt
      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)
  • aqualine ultimate style avatar for user Luke
    How would you graph x=4?
    (5 votes)
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  • blobby green style avatar for user Shaun Renee
    Is 6/8 greater than 6/10
    (3 votes)
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  • aqualine tree style avatar for user neelswapm
    I don't get the concept of the closed and open circle??
    (4 votes)
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    • orange juice squid orange style avatar for user Daberculosis
      Think of the open and closed circles as your hand. If your hand is open, you can't grasp anything or "contain" any object. This is kind of like 5 < x. The circle will be open because it does not contain the 5 because x is "greater than" 5. x has to be greater than 5, so 5 is not an answer to the inequality. Now if your hand is closed around an item you can contain it within your hand. For an inequality example, let's use 2 ≥ x. the circle is closed because 2 is contained and agrees with the inequality given. 2 is a solution because 2 is greater than or EQUAL TO x.
      (6 votes)
  • blobby green style avatar for user Malak Abdulwahab
    How i can solve this:
    16< |6-3x| < 19 ?
    (4 votes)
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  • starky seedling style avatar for user 3209jones
    I Love Math WOOWOO! GO MATH!
    (5 votes)
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Video transcript

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.