Activity 4.1 - Writing and Graphing Inequalities

By Shannon Bowen

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Understanding Inequality Statements

Writing Inequalities

Multiple Choice

 What is this inequality? $$\le$$

• Greater than

• Less than

• Greater than or equal to

• Less than or equal to

Multiple Choice

 What is this inequality? $$>$$

• Greater than

• Less than

• Greater than or equal to

• Less than or equal to

Multiple Choice

 What is this inequality? $$<$$

• Greater than

• Less than

• Greater than or equal to

• Less than or equal to

Multiple Choice

 What is this inequality? $$\ge$$

• Greater than

• Less than

• Greater than or equal to

• Less than or equal to

Multiple Choice

 Write the inequality for the word problem below:

The temperature today is less than yesterday's low temperature of  $$13\degree$$ .

• $$t<13$$  

• $$t>13$$  

• $$t\le13$$  

• $$t\ge13$$  

Multiple Choice

How would I write "a number less than OR equal to 2"

• $$x<2$$

• $$x>2$$

• $$x\le2$$

• $$x\ge2$$

Multiple Choice

Which inequality represents the real-world situation below?

“Doctors say you should exercise at least 30 minutes every day.”

• x $$<$$ 30

• x $$>$$ 30

• x $$\le$$ 30

• x $$\ge$$ 30

Multiple Choice

There are more than twenty students in the hallway.

• s>20

• s<20

• s=20

• The number of students in the hallway cannot be represented by any of the above choices.

Multiple Choice

The temperature is less than -4 degrees fahrenheit.

Can the temperature be exactly -4 degrees Fahrenheit?

• Yes

• No

Multiple Choice

You are in at least 5 of the photos

Is the number 5 included?

• Yes

• No.

Multiple Choice

You are in at least 5 photos.

List all the numbers below that make this statement true

0 1 2 3 4 5 6 7

• 5

• 5, 6, 7

• 0, 1, 2, 3, 4,

• 0, 1, 2, 3, 4, 5, 6, 7

Multiple Choice

X is a number such that $$x\le\frac{5}{2}$$  

Can the number be exactly $$\frac{5}{2}$$  

• Yes

• No

Multiple Choice

More than 3 students in our school are in the chess tournament.

Is the number 3 included?

• Yes

• No

Open Ended

More than 3 students from our school are in the chess tournament.

List all the numbers below that make this statement true

-3 -2 -1 0 1 2 3 4 5 6

Multiple Choice

X is a number such that X > -1.5

Can the number be exactly -1.5

• Yes

• No

Multiple Choice

What does the inequality say?

$$x\ge14$$

• a number greater than or equal to 14

• a number greater than 14

• a number less than or equal to 14

• a number less than 14

Understanding Inequality Symbols

Read the statement and answer the questions.

Writing and Graphing Inequalities

For each graph, write an inequality.

How to graph inequalities:

#1:  Decide if there should be an open of closed circle on the number

• Less than  ------ open circle

• Greater than  ----- open circle

• Less than or equal to ----- closed circle

• Greater than or equal to  ----- closed circle

How to graph inequalities:

#2:  Decide if the line should be shaded to the left or to the right on the numberline

• Lesser values extend left on the numberline.

• Greater values extend right on the numberline.

Multiple Choice

When graphing an inequality, you use an open dot when you use which symbol?

• <, >

• ≤, ≥ 

Multiple Choice

When graphing b< 6 would you use an open or closed circle?

• Open

• closed

Multiple Choice

When you graph an inequality, you used a closed dot when you use which symbols?

• ≤, ≥ 

• <, >

Multiple Choice

Would I use a closed circle or an open circle on the number line for $$x\ge7$$ ?

• Closed (shaded) circle

• Open (unshaded) circle

Multiple Choice

 Would I use a closed circle or an open circle on the number line for  $$x<6$$ ?

• Closed (shaded) circle

• Open (unshaded) circle

Multiple Choice

 Use what you know about the direction of the arrow...which direction will the arrow point for  $$x\le5$$ ?

Multiple Choice

 Use what you know about the direction of the arrow...which direction will the arrow point for $$x\ >10$$ ? 

Multiple Select

If the arrow is pointing as shown, which inequalities could it be graphing?

*Choose 2 answers*

• $$x<8$$

• $$x\le8$$

• $$x>8$$

• $$x\ge8$$

Multiple Choice

Which graph matches the inequality
k < 3?

• A

• B

• C

• D

Multiple Choice

Which graph matches the inequality
r ≥ -6?

• A

• B

• C

• D

Multiple Choice

Which graph matches the inequality 
x < -1.1?

• A

• B

• C

• D

Multiple Choice

Which inequality matches the graph?

• A

• B

• C

• D

Multiple Choice

What inequality does the number line graph represent?

• x ≥ 3

• x > 3

• x < -3

• x ≤ 3

Multiple Choice

What inequality does the number line graph represent?

• x ≤ 4

• x ≥ -4

• x < -4

• x < 4

Multiple Choice

The band practice will be less than 45 minutes long on Friday. Which inequality represents this situation?

• p < 45

• p > 45

• p ≤ 45

• p ≥ 45

Open Ended

Write an inequality for the number line.

Open Ended

Write an inequality for the number line.