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Course: 6th grade > Unit 7
Lesson 7: Intro to inequalities with variables- Testing solutions to inequalities
- Testing solutions to inequalities (basic)
- Plotting inequalities
- Plotting an inequality example
- Graphing basic inequalities
- Inequality from graph
- Plotting inequalities
- Inequalities word problems
- Inequalities word problems
- Graphing inequalities review
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Graphing inequalities review
Review graphing inequalities with variables on number lines, and then try some practice problems.
Inequalities
Inequalities show the relation between two expressions that are not equal.
Below are some examples of inequalities:
Inequalities symbols
Symbol | Meaning |
---|---|
Greater than | |
Greater than or equal to | |
Less than | |
Less than or equal to |
Graphing inequalities with variables
We can use a number line to show the possible solutions to an inequality.
Example 1:
An inequality like tells us that can be any value greater than .
We can show this on a number line by putting an open circle on and shading the numbers that are greater than .
Example 2:
If we have either the or symbol in our inequality, we shade in the circle to show that the variable may be equal to that number.
For example, is graphed as follows:
This number line shows that is either equal to or less than .
Want to learn more about graphing inequalities? Check out this video.
Practice
Want to try more problems like this? Check out these exercises:
Inequality from graph
Plotting inequalities
Inequality from graph
Plotting inequalities
Want to join the conversation?
- ok so umm we have to find the inequalities by know what's less than and greater than right?(29 votes)
- Yes, does this mean you get the two confused? If you make the sign with your left hand (<), left is less. If you make the sign with your right hand (>), Tony the Tiger says right is Grrrrrrrrreater.(46 votes)
- i dont understand why circles need to be full or hollow(5 votes)
- Full circle means we include the number:
X ≥ 3 This means X can be 3 OR greater
Hollow circle means we do NOT include the number:
X > 3 This means X can ONLY be greater than 3(34 votes)
- Whats a good way to memorize which way the line on the number line goes? I keep forgetting.(4 votes)
- If the variable is on the left, the inequality tells you which way to draw the line. For example:
x<6
Notice the inequality is pointing to the left, so your line goes to the left.
x>6
Notice the inequality points to the right, the line goes to the right.
Alternatively, you need to know that the smaller numbers are on the left of the number line and the larger numbers are to the right. A common tip used to help students remember what each inequality symbol means it to think of the symbol as the mouth of a hungry alligator. Its open mouth will always face the larger value.
6>x
Notice, the alligator wants to eat the 6 so it is larger than x. So, x must be numbers smaller than 6 and your line would get drawn to the left.
6<x
Notice, the alligator wants to eat the X, so the x is larger than 6 and your line needs to be to the right of the 6.
Hope this helps.(11 votes)
- i dont get it please help(3 votes)
- If we have x > a, then we shade the area on the right, and put an open circle on a.
If we have x ≥ a, then we shade the area on the right, and put a filled circle on a.
If we have x < a, then we shade the area on the left, and put an open circle on a.
If we have x ≤ a, then we shade the area on the left, and put a filled circle on a.
In case you are still confused, I have created an inequality plotter. Check it out:
https://www.khanacademy.org/computer-programming/single-variable-compound-inequalities-plotter-number-lines/6342204304572416
Tip: You can simply substitute x as a random number, and if it holds true, then shade the area on that side. Or else shade the other side.
For example if we have x > 4, we randomly select one point, let's say x = 0.
Substitute x = 0, and since 0 isn't larger than 4, we know the shaded area must not be on the side with 0, i.e. must not be on left side.(7 votes)
- How do you know if a word problem wants us to have the circle opened or closed? Are there key words, or certain things we have to look for?(6 votes)
- if the problem is a <> with the line under which means equal too, as well. You close the circle since you include the number.(2 votes)
- I dont understand some of the questions(4 votes)
- some of them are to trick you reread them(3 votes)
- Why does the open and close circle needed??(3 votes)
- These show if the point counts (closed circle and use of ≥ or ≤) or does not count (open circle and use of < or >). On a coordinate plane, it turns into an solid line or a dashed line.(4 votes)
- I don´t understand some of the questions(4 votes)
- Some are meant to trick you just reread the problem.(2 votes)
- how is that the answer my teacher is telling me different(3 votes)
- Teachers have different teaching ways, you should stick with what is taught, or watch mr.jay math on YouTube!(2 votes)
- so when i get down with the question it takes a while to pull the next quiz(3 votes)