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Inequalities•Notes Pages•Practice•Assessments

Includes Word Problems!

Rewrite and Solve the Inequality Graph the Solutions of the Inequality

Solutions Explained in Words

Check One Solution x + 5 < 8

Example

x + 5 < 8 -5 -5

x < 3 1 2 3 4 5

x + 5 < 82 + 5 < 8 7 < 8

I can add any number less than 3 to 5, and I’ll get a

number less than 8 It works!

These worksheets can be used in many ways.

I used these for two lessons:Day #1 - Solving and GraphingDay #2 - Writing Inequalities From Word Problems

I varied how I used the worksheets, depending on the ability of my students. In some classes, I gave out the more challenging problems to the students who needed it. In other classes, I gave them all the problems and let them choose a certain number to complete.

In all of my classes, students had the most difficult time checking their solutions. I had to spend extra time on it.

The word problems lead to great discussions about rounding up or rounding down!

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Solving and Graphing Inequalities Notebook Pages

Explain the solutions in words.Choose a number from the solutionson the graph to substitute and check.

Copy and solve the inequality (show your work). Label and graph the solutions to the inequality.


x + 3 > 7


4m ≤ 12

Describe the meaning of the following symbols:

> ≥< ≤

©2015 Math on the Move

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Name DateSolving and Graphing One-Step Inequalities




x + 5 < 8




y + 2 ≥ 11

4m > 20


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Learning Target: I can solve a multiplication or division inequality involving negative integers.

Explore and Discover

Simplify each inequality by substituting the given value for y. Then write whether the resulting inequality is TRUE or FALSE

2y < 4

Check the same values for y, using the following inequality. Write whether the resulting inequality is TRUE or FALSE

-2y < 4

Compare your solutions from both inequalities. What are some similarities and differences you see?


y = -3 y = 0

y = -1 y = -6

y = -3 y = 0

y = -1 y = -6

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Notes

When multiplying or dividing both sides of an inequality by a negative number,

______________________________Examples:

-2y < 4

-6x > 48

≥ 4x

-6

Try it Out:

≥ -7x

-5

Circle the inequalities that would require you to change the inequality symbol:

5y < -12

-2m > 8

x - 3 ≤ -8

≥ -4k

3

1 3

g≤ -2-

-2y + 3 > -9


Check the TRUE/FALSE solutions from our exploration page!

H

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Name DateSolving and Graphing Inequalities(negative coefficients)







-5y > 20

-3y + 2 ≤ 17

-2x + 5 < 13


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Name DateSolving and Graphing Multi-Step Inequalities







-2x + 7 ≥ 13

-3y + 2y < 2

4(x + 2) ≤ 8


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One-Step Inequalities Word Problems Name Date

Explain the solutions in words.Choose a solution to check.


Rick won 27 tickets playing a game. To get a prize, he needs to win at least 30 tickets. How many more tickets can he win to get a prize?



Bracelets cost $3 each. Rachel can spend no more than $20. How many bracelets can she buy?



Max earns $9 per hour. This week he’s hoping to earn at least $200. How many hours would he need to work?


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Two-Step Inequalities Word Problems Name Date



Jaime has $32. He starts shoveling driveways and earns $7 per driveway. He needs at least $75 to buy a skateboard he wants. How many driveways does he need to shovel?



A taxi charges a $3 fee and charges $.75 per mile. Angela can spend no more than $20. How many miles can she travel in the taxi?



Alex has $30 saved and he earns $12 per hour. He wants to have at least $150 in his savings account. How many hours can he work?


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Solving And Graphing One-Step Inequalities - Exit Slip


x - 5 ≤ 4


Name Date

Which of the four sections is the easiest for you? Which is the most difficult? Explain.

Solving And Graphing One-Step Inequalities - Exit Slip


x - 5 ≤ 4


Name Date

Which of the four sections is the easiest for you? Which is the most difficult? Explain.


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Solving And Graphing One-Step Inequalities(with negative coefficients) - Exit Slip


-2y ≤ 14


Name Date

Describe the steps you took to solve the inequality. Explain why you did each step.

Solving And Graphing One-Step Inequalities(with negative coefficients) - Exit Slip


-2y ≤ 14


Name Date

Describe the steps you took to solve the inequality. Explain why you did each step.


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Writing, Solving and Graphing Inequalities(from word problems) - Exit Slip Name Date

What is the difference between the phrases “at least” and “at most”? Give an example of each.

Writing, Solving and Graphing Inequalities(from word problems) - Exit Slip Name Date



Becki charges $6 an hour to babysit. She is saving to buy a new phone. She needs at least $200. How many hours does she need to babysit?



Becki charges $6 an hour to babysit. She is saving to buy a new phone. She needs at least $200. How many hours does she need to babysit?

What is the difference between the phrases “at least” and “at most”? Give an example of each.


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Explore and Discover

Simplify each inequality by substituting the given value for y. Then write whether the resulting inequality is TRUE or FALSE

2y < 4

Check the same values for y, using the following inequality. Write whether the resulting inequality is TRUE or FALSE

-2y < 4

Compare your solutions from both inequalities. What are some similarities and differences you see?


y = -3 y = 0

y = -1 y = -6

y = -3 y = 0

y = -1 y = -6

2(-3) < 4 -6 < 4 TRUE

2(0) < 4 0 < 4 TRUE

2(-1) < 4 -2 < 4 TRUE

2(-6) < 4 -12 < 4 TRUE

-2(-3) < 4 6 < 4

FALSE

-2(0) < 4 0 < 4 TRUE

-2(-1) < 4 2 < 4 TRUE

-2(-6) < 4 12 < 4 FALSE

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NameInequalities Practice - #1



Check One Solution from Graph x + 5 < 8



Check One Solution from Graph 4y > 20



Check One Solution from Graph y + 2 ≥ 11

Key

x < 3

y > 5

y ≥ 9


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Check One Solution from Graph -2x + 5 < 13



Check One Solution from Graph -5y > 20



Check One Solution from Graph -3y + 2 ≤ 17

x > -4

y < -4

y ≥ -5


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Check One Solution from Graph 4(x + 2) ≤ -8



Check One Solution from Graph -2x + 7 ≥ 13



Check One Solution from Graph -3y + 2y < 2


x ≤ -4

x ≤ -3

y > -2


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Write and Solve the Inequality Graph the Solutions of the Inequality


Check One Solution from Graph

Rick won 27 tickets playing a game. To get a prize, he needs to win at least 30 tickets. How many more tickets can he win to get a prize?




Bracelets cost $3 each. Rachel can spend no more than $20. How many bracelets can she buy?




Max earns $9 per hour. This week he’s hoping to earn at least $200. How many hours would he need to work?

NameInequalities Word Problem - Practice #1

t + 27 ≥ 30t ≥ 3

3b ≤ 20b ≤ 6.66

b ≤ 6

9h ≥ 2009h ≥ 22.2

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Jaime has $32 in his savings account. He starts shoveling driveways and charges $7 per driveway. He needs at least $75 to buy the skateboard he wants. How many driveways does he need to shovel?




A taxi charges a $3 fee and charges $.75 per mile. Angela can spend no more than $20. How many miles can she travel in the taxi?




Alex has $30 saved and he earns $12 per hour. He wants to have at least $150 in his savings account. How many hours can he work?

NameInequalities Word Problem - Practice #2

7d + 32 ≥ 75d ≥ 6.14

d ≥ 7

Jaime has to shovel 7 or more driveways. He can’t shovel part of a

driveway, and 6 would not be enough.

.75m + 3 ≤ 20m ≤ 22.66

m ≤ 22

Although Angela could pay for part of a mile, she might want to stay under 22

miles to make sure she doesn’t go over (and to leave room for a tip!)

12w + 30 ≥ 150w ≥ 10

Alex has to work 10 or more weeks in order to have $150 in savings

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