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Operations and Algebraic Thinking 218-221

Course: Operations and Algebraic Thinking 218-221>Unit 5

Lesson 7: 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, is greater than, 7
6, space, start underline, is less than, end underline, space, a, plus, 2
x, is less than, 5

Inequalities symbols

SymbolMeaning
is greater thanGreater than
start underline, is greater than, end underlineGreater than or equal to
is less thanLess than
start underline, is less than, end underlineLess 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, is greater than, 4
An inequality like x, is greater than, 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: y, space, start underline, is less than, end underline, space, 3
If we have either the start underline, is greater than, end underline or start underline, is less than, end underline symbol in our inequality, we shade in the circle to show that the variable may be equal to that number.
For example, y, space, start underline, is less than, end underline, space, 3 is graphed as follows:
This number line shows that y is either equal to 3 or less than 3.

Practice

Problem 1
• Current
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
• 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 understnd
• This is very wise, and relatable.
• 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.