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!

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?

when do you close the circle?1!

graph x is less than 4.0 lets draw yourself a number line

what does it mean when the dot is open on the 2 and the line is going both negative and positive ways?

It means that All Real Numbers except 2 is the solution.

For some reason, I cannot remember when to use an open circle, and when to use a solid dot on these number lines.

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.

why do you not stop at dot 3?

Because there are many fraction and decimals that sit in between 3 and 4. All values less than 4 are solutions. So, the graph needs to include numbers like 3.5; 3 5/8; 3.9999; etc. Hope this helps.

How would you graph x=4?

Vertical line going through 4 on x axis.

Would it still be x < 4 if you did not put a circle on 4?

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 "<=".

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6th grade

Course: 6th grade > Unit 7

Lesson 7: Intro to inequalities with variables

Plotting an inequality example

Name: Plotting an inequality example
Uploaded: 2011-02-20T16:40:20Z
Description: Drawing a number line helps visualize 'x is less than 4'. We mark 4 with a circle, not a dot, because 4 isn't included. Then, we color the line below 4, showing all values less than 4. Easy peasy, lemon squeezy

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Drawing a number line helps visualize 'x is less than 4'. We mark 4 with a circle, not a dot, because 4 isn't included. Then, we color the line below 4, showing all values less than 4. Easy peasy, lemon squeezy. Created by Sal Khan and Monterey Institute for Technology and Education.

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flawabud101
Posted 4 years ago. Direct link to flawabud101's post “Hello! Can anyone help me...”
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!
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(16 votes)
Answer
- David Severin
  Posted 4 years ago. Direct link to David Severin's post “Not sure if you know the ...”
  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?
  Comment on David Severin's post “Not sure if you know the ...”
  (11 votes)
Walker, Lauren
Posted 8 years ago. Direct link to Walker, Lauren's post “when do you close the cir...”
when do you close the circle?1!
Button navigates to signup pageComment on Walker, Lauren's post “when do you close the cir...”
(12 votes)
Answer
- Vraj
  Posted 7 years ago. Direct link to Vraj's post “graph x is less than 4.0 ...”
  graph x is less than 4.0 lets draw yourself a number line
  Comment on Vraj's post “graph x is less than 4.0 ...”
  (7 votes)
Gina Marquez
Posted 6 years ago. Direct link to Gina Marquez's post “what does it mean when th...”
what does it mean when the dot is open on the 2 and the line is going both negative and positive ways?
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(12 votes)
Answer
- Mr Henriques
  Posted 6 years ago. Direct link to Mr Henriques's post “It means that All Real Nu...”
  It means that All Real Numbers except 2 is the solution.
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  (6 votes)
Val B.
Posted 8 years ago. Direct link to Val B.'s post “For some reason, I cannot...”
For some reason, I cannot remember when to use an open circle, and when to use a solid dot on these number lines.
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(6 votes)
Answer
- Britt
  Posted 8 years ago. Direct link to Britt's post “I always remember: an ope...”
  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.
  Comment on Britt's post “I always remember: an ope...”
  (13 votes)
Marcimus
Posted 5 months ago. Direct link to Marcimus's post “why do you not stop at do...”
why do you not stop at dot 3?
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(6 votes)
Answer
- Kim Seidel
  Posted 5 months ago. Direct link to Kim Seidel's post “Because there are many fr...”
  Because there are many fraction and decimals that sit in between 3 and 4. All values less than 4 are solutions. So, the graph needs to include numbers like 3.5; 3 5/8; 3.9999; etc.
  
  Hope this helps.
  Button navigates to signup page
  (8 votes)
3209jones
Posted 2 years ago. Direct link to 3209jones's post “I Love Math WOOWOO! GO MA...”
I Love Math WOOWOO! GO MATH!
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(7 votes)
Answer
- Tanner Abercrombie
  Posted 8 months ago. Direct link to Tanner Abercrombie's post “Good for you if you love ...”
  Good for you if you love math so much than ask a math question or make a math statement.
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  (0 votes)
David White
Posted 5 months ago. Direct link to David White's post “Would it still be x < 4 i...”
Would it still be x < 4 if you did not put a circle on 4?
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(3 votes)
Answer
- Kim Seidel
  Posted 5 months ago. Direct link to Kim Seidel's post “The dot or circle is alwa...”
  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 "<=".
  Comment on Kim Seidel's post “The dot or circle is alwa...”
  (7 votes)
Luke
Posted 8 years ago. Direct link to Luke's post “How would you graph x=4?”
How would you graph x=4?
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(5 votes)
Answer
- Michal Valeš
  Posted 8 years ago. Direct link to Michal Valeš's post “Vertical line going throu...”
  Vertical line going through 4 on x axis.
  Comment on Michal Valeš's post “Vertical line going throu...”
  (3 votes)
Matzke
Posted 4 months ago. Direct link to Matzke's post “thanks for help”
thanks for help
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(6 votes)
Answer
jacampbell29
Posted 5 months ago. Direct link to jacampbell29's post “Graph x is less than 4. S...”
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.
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(6 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.