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## MAP Recommended Practice

### Course: MAP Recommended Practice>Unit 17

Lesson 27: Intro to inequalities with variables

# 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:
$9>7$
$x<5$

### Inequalities symbols

SymbolMeaning
$>$Greater than
$\underset{―}{>}$Greater than or equal to
$<$Less than
$\underset{―}{<}$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: $x>4$
An inequality like $x>4$ tells us that $x$ can be any value greater than $4$.
We can show this on a number line by putting an open circle on $4$ and shading the numbers that are greater than $4$.
Example 2:
If we have either the $\underset{―}{>}$ or $\underset{―}{<}$ 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 $y$ is either equal to $3$ or less than $3$.

## Practice

Problem 1
Choose the inequality that represents the following graph.

Want to try more problems like this? Check out these exercises:
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?
• 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.
• The questions were easy, but didn't really make me think. And if i do get those my teacher should only assign like 3
• Most of the questions were easy however my teacher loves to assign few but very tricky questions.
• i dont understand why circles need to be full or hollow
• 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
• what is this usefull for my life? exept for not loosing maths but WHY
• We never know. Don't waste your time with those questions. You do not study to pass the maths. You study to make your brain stronger and faster. When the future problem comes, you will be able to decide if inequalities will be needed or not and will solve then.
• Whats a good way to memorize which way the line on the number line goes? I keep forgetting.
• 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.
• I dont understand some of the questions
• some of them are to trick you reread them
• 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?
• if the problem is a <> with the line under which means equal too, as well. You close the circle since you include the number.
• 2x-7y=30 what is x
• I don't know if it's actually possible to find the value of x in this equation without knowing what y is, but it might be helpful to start by getting x by itself

2x - 7y = 30 add 7y to both sides
2x = 30 + 7y divide both sides by 2
x = (30 + 7y)/2

but wait, what if we replace x with (30+7y)/2, because they're equal

We'd get
2((30+7y)/2)-7y=30
30+7y-7y=30
30=30...

wait never-mind. That's technically correct, but also entirely useless. I still don't know what x is.

If anyone knows if it's possible to find x with only this information, then let me know.
• I don´t understand some of the questions