THANK YOU FOR YOUR PURCHASE!...*NOTE: This file has been organized for double-sided printing. Any blank pages were left so intentionally to make printing easy. Ideas for Implementation:

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CLIPART AND FONT ATTRIBUTION

Maneuvering the Middle resources include clipart and fonts from the following designers.

M A N E U V E R I N G T H E M I D D L E .C O M

PA G E T W O

PAGE TOPIC RESOURCE

4 Sample Pacing Guide

5-6 Ideas for Implementation & Helpful Hints

7-16 Binder Covers, Dividers, and Spine Labels

17-18 Simplifying Expressions Student Handout 1

19 Simplifying Expressions Homework 1

21-22 Solving One-Step Equations Student Handout 2

23 Solving One-Step Equations Homework 2

25-26 Solving Two-Step Equations Student Handout 3

27 Solving Two-Step Equations Mini-Quiz 1

29-30 Solving Two-Step Equations with Rationals Student Handout 4

31 Solving Two-Step Equations with Rationals Homework 3

33-34 Writing and Solving Equations in Real Life Student Handout 5

35 Writing and Solving Equations in Real Life Homework 4

37-38 Equations Quiz Quiz 1

39-40 Intro to Inequalities Student Handout 6

41 Intro to Inequalities Homework 5

43-44 Solving Two-Step Inequalities Student Handout 7

45 Solving Two-Step Inequalities Homework 6

47 Inequalities Quiz Quiz 2

49-50 Writing Inequalities Student Handout 8

51 Writing Inequalities Homework 7

53-54 Solving Inequalities in Real Life Student Handout 9

55 Solving Inequalities in Real Life Homework 8

57-60 Equations & Inequalities Unit Study Guide Study Guide

61-62 Equations & Inequalities Unit Test Test

EQUATIONS & INEQUALITIES UNITTable of Contents

©Maneuvering the Middle LLC, 2017


EQUATIONS AND INEQUALITIES UNITPACING GUIDE

DAY 1 DAY 2 DAY 3 DAY 4 DAY 5

Simplifying Expressions

Solving One-Step Equations

Solving Two-Step Equations

Solving Two-Step Equations with

Rationals

Writing and Solving Equations in Real-Life

Student Handout 1Homework 1


Student Handout 3Mini-Quiz 1



DAY 6 DAY 7 DAY 8 DAY 9 DAY 10

Solving Equations Quiz Intro to Inequalities Solving Two-StepInequalities

Solving Inequalities Quiz

Writing Inequalities

Quiz 1 Student Handout 6Homework 5


Quiz 2 Student Handout 8Homework 7

DAY 11 DAY 12 DAY 13 NOTES

Solving Inequalities in Real Life

Equations and Inequalities Unit Study

Guide

Equations and Inequalities Unit Test

The homework and student handout numbers are intentionally off in order to compensate for the mini-quiz. This way it does not appear that there is a missing homework assignment in the grade book.


Unit Study Guide Unit Test

*NOTE: This file has been organized for double-sided printing. Any blank pages were left so intentionally to make printing easy.

Ideas for Implementation: This bundle has all of the notes, homework, quizzes, and tests to make your life easier and help your students to be successful with equations and inequalities. A sample pacing guide is included for those of you who do not have a district scope and sequence or if it is very general. Additionally, an answer key is included.

If you notice any discrepancies in the documents or have any questions, please email me at: [email protected].

READINESS7.11A Model and solve one-variable, two-step equations and inequalities.

SUPPORTING7.10A Write one-variable, two-step equations and inequalities to represent constraints or conditions within problems.

7.10B Represent solutions for one-variable, two-step equations and inequalities on number lines.

7.10C Write a corresponding real-world problem given a one-variable, two-step equation or inequality.

7.11B Determine if the given value(s) make(s) one-variable, two-step equations and inequalities true.

7.11C Write and solve equations using geometry concepts, including the sum of the angles in a triangle, and angle relationships.

EQUATIONS & INEQUALITIESStudent Handouts


HELPFUL HINTSA few ideas for organizing your curriculum and keeping things nice and neat:

Keep each unit in a separate binder, and use the spine labels and covers to keep them looking nice and easy to find. I personally love 1.5” binders.

Student Handouts

BINDERS

I place my originals in page protectors in chronological order. Any extra copies from that lesson I hole punch and place behind that page. When I need an extra, or when a student is missing something from weeeeeeeeks ago, I can simply pull out a copy.

PAGE PROTECTORS

I highlight the edges of my answer keys, or if I am really good, print them on colored paper. It helps them to stand out and makes it easy to find on my desk, in a binder, by the document camera, etc. Plus, highlighter doesn’t show up if you make a copy.

ANSWER KEYS

Card stock in a page protector makes an awesome divider. When I set up my dividers, I include one each for handouts, activities, assessments, and answer keys. Binder covers and spine labels have been included. J

CARD STOCK

Happy Teaching!


EQUATIONS &INEQUALITIES

s e v e n t h G r a d e C u r r i c u l u m

U n i t F O U R : 7 . 1 0 A - C 7 . 1 1 A - C

©MANEUVERINGTHEMIDDLE,2017

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U n i t F O U R : A N S W E R K E Y S




U n i t F O U R : A C T I V I T I E S




U n i t F O U R : A S S E S S M E N T S


SIMPLIFYINGEXPRESSIONS

• Terms can be classified as ______________ or ______________, and

expressions can be simplified by combining like terms.

• Like terms must have the same ______________and ______________.

Ex: 7x and 9x are like terms

4d and 4g are not like terms

Name _____________________________________Date ______________________________Pd______

Unit: Equations & InequalitiesStudent Handout 1

SIMPLIFYING EXPRESSIONSAn expression is a mathematical phrase that can contain ______________, ______________,

and ______________.

EXAMPLES LIKE TERMS

8c, 16, -8c, -16b

12, -12x, 12x

9y, 5z, 9w

11g, 11, -7g

0.5t, 1.5t, 2.5

1m, n, m, 1

4b, b, 7, 9b

0, -8, 13r


-6x + 12

In the left table below, determine which of the terms are like terms. In the right table below, determine if the terms are like or unlike.

EXAMPLES LIKE OR UNLIKE

29, 292

b, 3b

6, 9

-3r, -3p

13k, 13k2

c, c4

c, 4c, 8c

16, 0, -9

Use the expression below to label the various parts of the expression.

The Robinson family ordered snacks at the State Fair. They bought the following drinks (d),

pizza (p), and ice cream cones (c).

a. Write an expression to represent their purchases: _____________________________________

b. Simplify the expression by combining like terms: _______________________________________

c. Explain how this example can relate to an algebraic expression.

______________________________________________________________________________________

______________________________________________________________________________________

Summarize today’s lesson:

Only like terms can be _________________ in order to simplify an expression.

Practice simplifying the expressions below by combining like terms.

1. 7a – 6 + 8a

2.14b + 6b – 12

3.20c + 8d + 10c – 5d

4.-3d + 8d – 5d

5.3e – 19 – 7e + 10

6.-4f – 9 – f + 15

7.1.5g – 10 + 6.5g – 3

8.1

2h + 2h +

3

2h − 1

9.4.2j + 6.7j – 5j – 5


6.4r + 9r – 11r + 7r

7.-r + 6 + 8r – 14

8.-26r + 7r – 15p – 7p

9.8r + 12p – 7 – 3p

10.10r – 5r + 3r – 8r

11.-4p – 2r – 15p

12.3

4r + 2r +

1

2r

13.1.5r – 3r + 8r + 2.5r

14.2

3p +

4

3p –

1

3p

Name _____________________________________Date ______________________________Pd______

Unit: Equations & InequalitiesHomework 1


List three terms that are like the given terms below.

GIVEN TERM LIKE TERMS

1.

2.

3.

4.

5.

−19m

28

42bc

−y

2r

Simplify the expressions by combining like terms.

SIMPLIFYING EXPRESSIONS

INVE

RSE

OPE

RATI

ONS + −

× ÷WHAT IS THE

INVERSE OF THAT OPERATION?

WHAT OPERATION IS TAKING PLACE?

SOLVING ONE-STEP

EQUATIONS

• In order to solve an equation, we must _________________ the variable

and keep each side of the equation ________________ .

• We can use inverse operations to move terms from one side of the

equation to the other.

• Inverse operations can be thought of as _________________ or “undoing”

____________ .

Name _____________________________________Date ______________________________Pd______


SOLVING ONE-STEP EQUATIONS

Use inverse operations to solve each one-step equation below.

1.4x = 16

2.x + 9 = 13

3.x – 8 = 14

4.x

5 = 13

5.x – 6 = 11

6.2x = 88


One-step equations can also include _________________ and decimals.

7.6x = 16

8.x + 2.5 = 7.5

9.2

3x = 8

10.x

3 = 7

11.x + 1.6 = 8.2

12.4x = 2.8

13. If a chocolate cake is divided into six equal slices and each slice has 280 calories, how many calories are in the whole cake?

I KNOW: I NEED TO KNOW:

PLAN AND WORK: MY SOLUTION:


14. Pedro made a pot of coffee for some friends. He served 34 ounces to his friends and then measured that there were 20 ounces leftover. How much coffee did Pedro make?




Name _____________________________________Date ______________________________Pd______


SOLVING ONE-STEP EQUATIONSSolve each of the equations below. Be sure to check your work.

1.-7x = 63

2.x + 8 = -15

3.2

3x = 27

4.x

9 = −5

5.x + 2.6 = 1.7

6.-8x = -56

Read each problem below. Write an equation to represent the situation and then solve.

7. Olivia purchases gifts for her mom and grandma for Mother’s Day. The first is a pair of sunglasses for $16.35 and the second is a bracelet. Her total is $39.75. How much did she spend on the bracelet?

Variable: ____________________________

Equation: ____________________________

Solution: ____________________________

8. Alana and two of her friends evenly split the cost of a meal. They determine that each person owes $14.68. How much was the entire cost of the meal?

Variable: ____________________________

Equation: ____________________________

Solution: ____________________________

9. Samuel is six inches taller than his brotherElijah. If Samuel is 48 inches tall, how tall is Elijah?

Variable: ____________________________

Equation: ____________________________

Solution: ____________________________

10. Jeff drank 15 ounces of Gatorade after running a race. There were 20 ounces left. How much Gatorade was originally in the container?

Variable: ____________________________

Equation: ____________________________

Solution: ____________________________

Name _____________________________________Date ______________________________Pd______


SOLVING TWO-STEP EQUATIONS

Solve each two-step equation below. Then, prove that your answer is correct.

1.10 + 3k = 22

2.19 = 4p - 5

3.r

2 − 8 = 16

✓ CHECK: ✓ CHECK: ✓ CHECK:

SOLVING TWO-STEP EQUATIONS

1. Undo addition or subtraction with the ________________ operation.

2. Undo multiplication or ________________ with the inverse operation.

3. Isolate the ________________ .

4. Check your ________________ .


x x1

1

1

1

1

11=

Use the models below to solve the equation.

x x x1

1

1

1=

1

1 1

1

1

1

DICE ROLL SOLVE SOLUTION

2 4x – 8 = 32

3 6x + 9 = 27

4 x

4 + 8 = 41

5 9x – 10 = 62

6 x

6 + 2 = 16

7 19 = 5 + 7x

8 x

3 – 14 = 9

9 8x – 54 = 82

10 42 = 6x – 24

11 10x + 25 = 50

12 58 = 7x – 5


Solve each equation below for practice. Roll a pair of dice, and find the sum of the two numbers showing. Solve that problem.

SHOW WORK HERE:


Name _____________________________________Date ______________________________Pd______

Unit: Equations & InequalitiesMini Quiz 1

©M

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LLC

, 2017

MINI-QUIZ: ONE- AND TWO-STEP EQUATIONS1. Solve.

6x – 9 = 332. Solve.

8 + x2= 12

5. Ty is eight inches shorterthan his brother, Reece. If Ty is 42 inches tall, then how tall is Reece?

Equation: _________________

Solution: _________________

3. Solve.3x = 105

4. Solve.x

3= 46

Name _____________________________________Date ______________________________Pd______

Unit: Equations & InequalitiesMini Quiz 1

©M

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ng t

he M

iddle

LLC

, 2017

1. Solve.6x – 9 = 33

2. Solve.

8 + x2= 12

5. Ty is eight inches shorterthan his brother, Reece. If Ty is 42 inches tall, then how tall is Reece?

Equation: _________________

Solution: _________________

3. Solve.3x = 105

4. Solve.x

3= 46

MINI-QUIZ: ONE- AND TWO-STEP EQUATIONS

Name _____________________________________Date ______________________________Pd______


SOLVING TWO-STEP EQUATIONS WITH RATIONALS


Equations with rational numbers can be solved just like any _______________, but you

must follow the rules for __________________________.

ADDING INTEGERS

• If the two values have the same sign, then _______________and use the same sign.

positive + positive = positive Ex: 6 + 5 = 11negative + negative = negative Ex: -6 + (-5) = -11

• If the signs are _______________, then _______________ and take the sign of the number with the greatest absolute value.

Ex: 6 + (-5) = 1 Ex: -6 + 5 = -1

SUBTRACTING INTEGERS

• Rewrite the problem to add the _______________.Then, follow the rules for adding integers.

Ex: 6 – 7 = -9 – 11 = -3 – (-8) =6 + (-7) = -9 + (-11) = -3 + 8 =

MULTIPLYING AND DIVIDING

INTEGERS

• Multiply or divide the two numbers.

• If the signs are the same, then the answer is ______________.

positive · positive = positive Ex: 6 · 5 = 30negative · negative = positive Ex: -6 · (-5) = 30

• If the signs are different, then the answer is ______________.

positive · negative = negative Ex: 6 · (-5) = -30negative · negative = negative Ex: -6 · 5 = -30

1.-6 + (-19) =

2.5 – 32 =

3.14 + (-27) =

4.-11 – 8 =

5.-8 & (-9) =

6.-14 & 3 =

7.−244

=

8.−35−7 =

Practice solving the following problems using the rules for integer operations.

17. Margo solves several equations and then states that all of them have a solution of x = 7. However, Kenneth disagrees. Determine which of the following equations have a solution of x = 7 and then justify your response.

______________________________________________________________________________________

______________________________________________________________________________________


Practice solving the equations below. Prove that your solution is correct by checking your work.

9.-4k + 9 = 32

✓ CHECK: 10.x

2– 14 = 20

✓ CHECK:


Use your understanding of two-step equations to solve the problems below.

11.3x + 8 = -10

12.-2x – 10 = 15

13.x

6+ 7 = −11

14.x

−3+ 20 = 30

15.-2x + 7 = -32

16.x

−2– 15 = −35

6x + 11 = 55

A

-3x – 18 = 39

B2x – 14 = -28

C

7x + 9 = 58

D

Name _____________________________________Date ______________________________Pd______


_________ _________________________________________________________

17x + 9 = 58

2-3x + 33 = -12

3x5+ 7 = 16

43x + 2 = -55

52x + 8 = -4

613 – 4x = -11

WHY DID THE OBTUSE ANGLE GO TO THE BEACH?

W L y T

C R I H

O E V G

A S D N

3 7 9 6 1 11 13 12 4 10 3 10 12 7 2 5 12 8 4 12 12 1


Solve each equation. Match the final answer to the letter below. Write the letter in the blank.

7x2– 12 = -14

88x + 16 = 8

9x−3 + 11 = 8

10-8x – 15 = 25

112x – 2 = -18

125x – 1 = 14

13x4+ 24 = 21

SOLVING TWO-STEP EQUATIONS WITH INTEGERS

x = 9

x = -2

x = -8

x = 6

x = 5

x = -19

x = 3

x = 7

x = 15

x = 45

x = -12

x = -6

x = -4

x = 2

x = -1

x = -5

Name _____________________________________Date ______________________________Pd______


SOLVING EQUATIONS IN REAL-LIFE





1. The width of a rectangle is two centimeters less than eight times the length. The perimeter is 68 cm. What are the width and length of the rectangle?

Variable: ____________________________

Equation: ____________________________

2. Stephanie is registering her son for swim lessons. There is a one-time $45 registration fee plus a $20 fee per lesson. Stephanie paid a total of $225. For how many lessons did Stephanie register?


Variable: ____________________________

Equation: ____________________________

Play tic-tac-toe with your neighbor. Xs __________________ Os _______________

Carefully read each problem, write an equation, and solve.


3. A plumber charges $55 for a service call plus $35 per hour. If the plumber’s bill was $160, how many hours was he there?

4. The length of a rectangle is twice the width. If the perimeter of the rectangle is 60 units, find the area of the rectangle.

5. The Nile River is 6,690 kilometers long. This is 1,160 kilometers longer than the Yangtze River. How long is the Yangtze River?

6. A waiter earns $128 for 6 hours of work. The total included $86 in tips. How much does the waiter earn each hour?

7. Three sisters each purchase adress of equal value. One of the sisters purchases a purse for $26.00. If the grand total was $249.50, how much did each dress cost?

8. Emma’s sister is nine years older than Emma. Their combined ages add up to 49. How old is Emma?

9. In one year, Michael read 18 books. This was four fewer than twice the number of books that Jeff read. How many books did Jeff read?

10. Samuel is saving to buy a watch that costs $169. This is $48 more than 4 times what he saved last month. How much did he save last month?

11. Mr. Martinez rents a car for one day. The charge is $36 plus $0.18 per mile. Mr. Martinez has a budget of $60. How many miles can he drive?


Name _____________________________________Date ______________________________Pd______


Answer the following questions. Be sure to justify your responses.


1. A student bought a juice pouch for $2.50 and 3 bags of chips. The total cost was $5.05. Write and solve an equation to determine the cost of a bag of chips, c.

Variable: ______________________________

Equation: ______________________________

Solution: ______________________________

2. Mr. Majors ordered six hot dogs and a bucket of popcorn at the concession stand. If the popcorn was $3.20, and the total was $18.20, what was the price of one hot dog?

Variable: ______________________________

Equation: ______________________________

Solution: ______________________________

3. The ages of three siblings are all consecutive integers. The sum of their ages is 39. How old is the youngest sibling?

Variable: ______________________________

Equation: ______________________________

Solution: ______________________________

4. The length of a rectangle is eight more than twice its width. The perimeter is 88 feet. Find the dimensions of the rectangle.

Variable: ______________________________

Equation: ______________________________

Solution: ______________________________

5. For a birthday party, Mr. Perkins orders 8 chocolate chip cookies and 16 sugar cookies. Each cookie is the same price. He also picks up a cupcake for himself, which costs $2.75. The total bill is $44.03. What is the cost of a cookie?

Variable: ______________________________

Equation: ______________________________

Solution: ______________________________

6. Mrs. Johnson just purchased a total of 12 books and magazines for her office. The total bill was $112. She spent $16 on magazines, and the books cost $12 each. How many books did she buy?

Variable: ______________________________

Equation: ______________________________

Solution: ______________________________

SOLVING EQUATIONS IN REAL-LIFE

Name _____________________________________Date ______________________________Pd______

Unit: Equations & InequalitiesQuiz 1

QUIZ: SOLVING EQUATIONSDetermine if the given value makes the equation true or false.

1. For 6x + 5 = 27, if x = 4 2. For x3– 8 = 15, if x = 69

Solve each of the following equations for the missing variable.

3. -3x + 9 = -18 4. 2x – 14 = -9

5. x2

+ 8 = -24 6. -2.5x – 10 = 40

Use the model to answer the question below.

7. The model below represents an equation. Which value of x makes the equation true?

A. x = 2 B. x = -2 C. x = 0.5 D. x = -0.5

Answers

1. ______________

2. ______________

3. ______________

4. ______________

5. ______________

6. ______________

7. ______________

8. ______________

9. _____________

10. _____________


x x x1

1

1

1

1

1=

1

1

1

1

1

1

1

1

8. A pizza shop charges $7.00 for a cheese pizza and $1.50 per topping. The total charge for Megan’s pizza was $11.50. Write and solve an equation to determine how many toppings Megan ordered on her pizza.

Variable: ______________________________

Equation: ______________________________

Solution: ______________________________

9. Mr. Andrews is trying to lose weight. He starts the year weighing 254 pounds. If he plans to burn enough calories to lose 4 pounds per week, then how many weeks will pass before Mr. Andrews weighs 228 pounds?

Variable: ______________________________

Equation: ______________________________

Solution: ______________________________

10. Ms. Bailey is taking her children and their friends to the movies. She will pay $10 for her adult ticket and $6 for each child ticket. Ms. Bailey spends $46.00 at the movies. Write and solve an equation to determine the number of child tickets Ms. Bailey purchases.

Variable: ______________________________

Equation: ______________________________

Solution: ______________________________


Set up and solve the real world problems below.

1. k + 8 ≥ 19, if k = 11 2. 12 > f, if f = 3 3. 3 > d, if d = 3

4. c – 12 > 30, if c = 13 5. 16 < b – 8, if b = 22 6. 6x + 5 < 18, if x = 5

7. 2j ≤ 8, if j = 5 8. 5r – 3 ≥ 25, if r = 6 9. 6m – 12 < 40, if m = 8

Determine whether each value makes a true statement.

Name _____________________________________Date ______________________________Pd______


INTRO TO INEQUALITIES

An equation uses an ______________ sign to show that both sides are _______________ .

An _________________ shows that both sides are ______ equal.

GREATER THAN GREATER THAN OR EQUAL TO LESS THAN LESS THAN OR

EQUAL TO NOT EQUAL

Use the _________________ as the starting point when reading inequalities.


Use an inequality symbol to create a true statement.

a. 4 ____ 9 b. 0.5 ____ 0.45 c. -3 ____ -2 d. -6.1 ____ -6.10 e. 12.4 ____ 12.04

Write a verbal description to represent the inequality statements below.

6 ≤ x: ______________________________________________________________________________

y < 0.5: ____________________________________________________________________________

1 2 3 4 5-1 0 1 2 315 20 25 30 35

3 4 5 6 710 11 12 13 14

10. k > 11

11. 12 ≥ f

12. d < 6

13. c < 25

14. 0 ≤ b

15. x ≥ 4.5

8 9 10 11 12

Practice graphing the following inequalities.

Inequalities can also be _________________ on the ______________________ .



INCLUDED NOT INCLUDED

Based on the verbal expression below, write and graph an inequality.

16. The McDonald family spends no more than $150 for groceries each week.

17. Jerod earns at least $10 per hour when mowing lawns.

0 2 3 4 5 61 87 9

x≤ 5

8 9 10 11 12 10 11 12 13 14 3 4 5 6 7

7. k ≤ 8 8. 13.5 ≥ f 9. d < 4

4.

________

5.

________

6.

________

1. k + 12 ≥ 20, if k = 15 2. -16 > -f, if f = 15 3. 9 > d, if d = 3

Name _____________________________________Date ______________________________Pd______



Based on the verbal expression below, write and graph an inequality.

10. The Parkland Zoo has a maximum capacity of 350 visitors (v).

11. Trina must spend at least 45 minutes (m) studying for her test.

INTRO TO INEQUALITIES

8 9 10 11 12 10 11 12 13 14 3 4 5 6 7

Substitute each variable to determine whether the inequality statement is true or false.

Write an inequality for each solution set graphed below.

Practice graphing the following inequalities:

1.10 + 3k ≤ 22

2.19 > -4p – 5

3.1

2r + 3 < 6

✓ CHECK: ✓ CHECK: ✓ CHECK:

Name _____________________________________Date ______________________________Pd______


SOLVING TWO-STEP INEQUALITIESTwo-step inequalities follow the same _______________for isolating the variable.

Think of it as “undoing” ______________.

Solve each two-step inequality below. Then, prove that your answer is correct.

5x + 9 < 17

SOLVING TWO-STEP

INEQUALITIES

1. Undo addition or subtraction with the ________________ operation.

2. Undo multiplication or ________________ with the inverse operation.

3. When you multiply or divide by a ______________number, the inequality

sign is ______________. (watch for negative signs)

3. Isolate the ________________.

4. Check the ________________ sign.

-2x – 3 > 13


DICE ROLL SOLVE SOLUTION GRAPH

2 4x – 8 < 32

3 -6x + 9 ≤ 25

4 3

4x + 8 < 41

5 2.5 x – 10 > 25

6 x

6 + 2 ≥ −16

7 -16 > 5 + 7x

8 6 + 1.5x < -12

9 -8x – 9 > -21

10 42 ≥ -6 + 3x

11 -10x + 25 ≤ 5

12 30 ≤ 3x – 5



Solve each equation below for practice. Roll a pair of dice, and find the sum of the two numbers showing. Solve that problem.

SHOW WORK HERE:


Name _____________________________________Date ______________________________Pd______


Match each of the inequalities to their appropriate graph Record your results below.

MATCH 1 MATCH 4

MATCH 2 MATCH 5

MATCH 3 MATCH 6

E

3x – 1 < -10

SOLVING TWO-STEP INEQUALITIES

Name _____________________________________Date ______________________________Pd______

Unit: Equations & InequalitiesQuiz 2

QUIZ: INEQUALITIESMatch each of the following inequality statements to the appropriate graph.

1. x > 6.5

2. − 12

≥ x

3. 6.5 > x

4. x > − 12

Evaluate whether each value makes a true or false statement.

5. k+ 6 ≥ 19, if k = 11 6. 16 < b + 8, if b = 22

Solve each inequality below.


Answers

1. ______________

2. ______________

3. ______________

4. ______________

5. ______________

6. ______________

7. ______________

8. ______________

9. _____________

10. _____________

11. _____________

12. _____________

7. -4x ≤ 32 8. 6x – 18 ≤ 27 9. x4

< -1.5

10. 5 + x2≥ 10 11. 10 + 2.5x > 35 12. 9 –x < -11

A.

B.

C.

D.

E.

-6 -4 -2 0 2

-1 1 3 5 7

2 4 6 8 10

-3 -2 -1 0 1

1 3 5 7 9

INEQUALITY PHRASES

Name _____________________________________Date ______________________________Pd______



WRITING INEQUALITIES

Verbal statements can be _________________ to algebraic inequalities, much like

deciphering a secret message or translating from one _________________ to another.

Translate each of the following into an algebraic inequality.

1. a number is at most fifteen 2. the sum of a number and three is less than twelve

3. the quotient of a number and negative two is greater than or equal to ten

4. four less than a number is at least negative six

5. the difference between a number and thirteen is atleast one

6. eight less a number is less than or equal to five

7. three times a number is more than negative seven

8. one-half of a number plus five is greater than eleven

9. negative six plus a number is less than or equal to fifteen

< > < >

Inequality: ___________________

Solution: _____________________

Graph:

Inequality: ___________________

Solution: _____________________

Graph:

Inequality: ___________________

Solution: _____________________

Graph:

Translate each statement into an algebraic inequality. Then, solve and graph the solution.



10. the sum of twice a number and four is at least 16

11. one-half of a number less six is greater than or equal to ten

12. three times a number increased by seven is less than eleven

13. the difference of two and a number is at least negative one

14. the quotient of a number and five is no greater than negative nine

15. twice a number less than twenty is at most ten

Inequality: ___________________

Solution: _____________________

Graph:

13. Which of the following inequality statements is represented by the graph below?

A. x – 2 ≤ 4 B. x2

+ 2 ≥ −6 C. -4 ≥ x D. x2≥ −2

Inequality: ___________________

Solution: _____________________

Graph:

Inequality: ___________________

Solution: _____________________

Graph:

-10 -8 -6 -4 -2

Name _____________________________________Date ______________________________Pd______


_______________ _________________________

1

Four more than three times a number is greater than twenty-two.

2

One less than five times a number is fewer than twenty-four.

3

Eight less a number is less than or equal to seventeen.

4

Negative ten is no less than two times a number plus fourteen.

WHAT IS A BIRD’S FAVORITE TYPE OF MATH?

L C GW O IB R PA E D

4 8 1 6 5 3 7 2


Match the phrases to the algebraic solution below. Then, write the letter in the blank below.

5

Twenty-seven is smaller than five times a number increased by seven.

6

A number divided by three less two is at most two.

7

The sum of eight times a number and negative four exceeds twelve.

8

The quotient of a number and negative one increased by eleven is less than or equal to fifteen.

x ≥ −4

5x < x < 6

x ≤12x > 3

x ≤ −12

x > 6

x ≥ −9 x > 2 x ≤ −9

x <11.5

x > 4

WRITING INEQUALITIES

Name _____________________________________Date ______________________________Pd______


SOLVING INEQUALITIES IN REAL-LIFE





1. Missy is saving to attend a week at summer camp. She needs $250.00 to register. Her

parents will contribute $75.00. She needs to raise the rest of the money babysitting for $12.00

per hour. What is the minimum number of hours she must babysit in order to attend camp?

2. The youth soccer team is fundraising by washing cars. They paid $84.55 for supplies. If they charge $8.00 per wash, how many cars must be washed to profit at least $300.00 dollars?







3. JoAnn has a bank account with $350.00 in it. Every week, she withdraws $12.50 to attend the movies. What is the maximum number of weeks that JoAnn can withdraw the money without allowing her bank account to drop below $210.00?

4. A jet ski rental charges a flat rate of $75, plus an additional $60 per hour. You do not want to spend more than $200. How many hours can you rent the jet ski and still be under budget?


Name _____________________________________Date ______________________________Pd______


Answer the following questions. Be sure to justify your responses.

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1. Marcus needs to bike at least 80 miles this week for his training. If he has already biked 25miles this week, then how many miles should he bike on each of the 5 remaining days this week?

Variable: ______________________________

Inequality: ______________________________

Solution: ______________________________

2. Jamal has $15.00 to spend at the concession stand. He buys nachos for $7.50, and he wants to purchase some Sour Straws for $1.50 each. How many Sour Straws can Jamal purchase with the money that he has?

Variable: ______________________________

Inequality: ______________________________

Solution: ______________________________

3. Taylor has a $30.00 gift card that she can spend at the store. She has already bought a $9.00 picture frame, and she wants to buy $3.00 journals with the leftover money on the card. How many journals can she buy without going over the card’s limit?

Variable: ______________________________

Inequality: ______________________________

Solution: ______________________________

4. Liza wants to have more than $750 in her

savings account before she will leave for college.

Right now she has $300, and she is going to

babysit to earn $12.00 an hour. How many hours

will Liza need to babysit before she leaves for

college?

Variable: ______________________________

Inequality: ______________________________

Solution: ______________________________

5. Dennis is selling chocolate bars for a fundraiser, and if he sells over $175 worth of candy, he’ll win a prize. If chocolates sell for $2.50 a bar, and Dennis has already sold $40 worth of candy, then how many more bars does he have to sell in order to win a prize?

Variable: ______________________________

Inequality: ______________________________

Solution: ______________________________

6. The amusement park won’t allow kids to ride roller-coasters until they are a minimum of 48 inches tall. Michael is now 42 inches tall, and grows about 1/2 inch every month. How many months will it be until Michael can ride a roller-coaster?

Variable: ______________________________

Inequality: ______________________________

Solution: ______________________________

SOLVING INEQUALITIES IN REAL-LIFE

Name _____________________________________Date ______________________________Pd______

Unit: Equations & InequalitiesReview

Solve each of the problems below. These represent the types of questions on your test. Be sure to ask questions if you need more help with a topic.

I CAN MODEL AND SOLVE TWO-STEP EQUATIONS. 7.11A

1.

-5x + 9 = 24

2.x

2 − 7= −10

3.

3x + 12 = 48

4.

-6x – 10 = 20

5.

12x – 17 = 33

6.x

4 + 5 = 25

7. Sketch a model to represent the equation

2x + 3 = 9. Then, solve the equation.

8. Sketch a model to represent the equation

3x + 9 = 3. Then, solve the equation.


EQUATIONS & INEQUALITIES UNIT STUDY GUIDE

I CAN DETERMINE IF A VALUE IS TRUE GIVEN AN EQUATION.

9. If x = -3, then which of the following equations are true? Circle all that are true.

A. x3− 9 = 15 B. 4x – 9 = -21

C. 6c + 9 = -13 D. -2x + 18 = 24

I CAN WRITE AND SOLVE TWO-STEP EQUATIONS GIVEN CONSTRAINTS. 7.10A

14. Felix joins a local recreation center to play basketball. The recreation center charges a $20 annual fee, plus an additional $15 per month for usage of the basketball courts. Felix prepays by writing a check for $185. Write an equation that can be used to determine m, the number of months Felix prepaid for. Then, solve the equation.

Equation: _______________________________

Solution: _______________________________

15. Asher weighs 15 pounds less than three times the weight of Audrey, his sister. Asher weighs 27 pounds. Write an equation that can be used to find w, the weight of Audrey. Then, solve the equation.

Equation: _______________________________

Solution: _______________________________


I CAN WRITE TWO-STEP EQUATIONS FROM REAL WORLD SITUATIONS. 7.10C

10. A home improvement store advertises 60 square feet of flooring for $287.00 including an $80.00 installation fee. Write an equation to represent the cost of one square foot of flooring.

Variable: ______________________________

Equation: ______________________________

11. A mom bought her kids 3 cartons of milkfor $1.25 each and 6 doughnuts. The total cost was $6.90. Write an equation to determine the cost of a doughnut.

Variable: ______________________________

Equation: ______________________________

12. Find the smaller of 2 consecutive integers, x, if the sum of the two integers is -29. Write an equation to determine the consecutive integers.

Variable: ______________________________

Equation: ______________________________

13. Mr. Peters just purchased a total of eight shrubs and trees for his yard. The total bill was $260. The shrubs cost $25 each and the trees cost $110 in total. Write an equation to determine the number of shrubs purchased.

Variable: ______________________________

Equation: ______________________________


I CAN SOLVE TWO-STEP INEQUALITIES. 7.11A

16.

-3x – 11 > 45

17.

10 – x ≤ 35

18.x

2− 8 ≥ 18

19.

30 < 2x - 6

20.

1.5x + 12 < 18

21.

16 ≥ 6 + x2

I CAN WRITE INEQUALITIES FROM REAL-WORLD PROBLEMS. 7.10C

22. Jasmine has a budget of $600.00 to spend on home renovations. She will spend $175.00 on a new sink and the remainder on countertops. The countertops cost $35 per square foot. What is the maximum number of square feet Jasmine can purchase?

Variable: ______________________________

Inequality: ______________________________

23. Hayden earns $9.50 per hour as a lifeguard. He earns a bonus of $50.00 for taking a training course. How many hours must he work to earn at least $300.00?

Variable: ______________________________

Inequality: ______________________________

24. Russell wants to buy three ties and a belt and must spend no more than $80.00. The belt costs $28.50. If the three ties are the same price, then how much can he pay for each tie?

Variable: ______________________________

Inequality: ______________________________

25. An online music service charges a $12.00 registration fee plus $1.50 for each song downloaded. If Mary Beth has a gift card with $60.00, then how many songs can she download?

Variable: ______________________________

Inequality: ______________________________

I CAN REPRESENT SOLUTIONS ON NUMBER LINES. 7.10B

26.4x – 9 < -18

27.7x + 22 > 15

28.-8x – 10 > -26

29.12x + 12 < 72


I CAN SOLVE REAL-WORLD INEQUALITIES. 7.EE.4

30. Megan is saving up to buy a new cell phone that costs $220.00. So far she has saved $175.00. Megan would like to buy the cell phone in four weeks. Write and solve an inequality to represent at least how much she must save every week to purchase the cell phone.

31. A warehouse holds 460 boxes. They ship out 65 boxes each week. After how many weeks will they have less than 100 boxes remaining? Write and solve an inequality that can be used to determine how many weeks it will take for the warehouse to have less than 100 boxes.

32. A 15-passenger van is rented for a family vacation. The van rental is $60.00 per day, plus a $145.00 insurance fee. How many days can the van be rented if they want to spend no more than $625.00 on the van rental? Write and solve an inequality.

33. Marco is limited to 7 hours of screen time each week. He decides to watch a movie that is 1 hour and 20 minutes on Sunday. If he divides the remainder of the time equally amongst the other six days, then how many minutes can he watch each day? Write and solve an inequality.

Name _____________________________________Date ______________________________Pd______

Unit: Equations & InequalitiesTest

Solve the problems below. Be sure to show your thinking.

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1. Solve.

50 = 2x + 12

x = ________

2. Solve.

-3x + 8 = 11

x = ________

3. Solve.

15x + 60 < 240

_____________________

4. Write an expression to represent the

perimeter of the figure below.

_____________________

5. A plumber charges $55 for a service call,

plus $35 per hour. If the plumber’s bill was

$160, then how many hours was he there?

_____________________

6. The perimeter of an equilateral triangle is

63 inches. If the length of each side is (4x+3),

find the value of x.

_____________________

7. A home improvement store advertises 60

square feet of flooring for $287.00, which

includes a $80.00 installation fee. Write an

equation to represent the cost of one square

foot of flooring.

_____________________

8. If x = -1, then which of the

following equations makes a

true statement?

A. 4x + 9 = 20

B. -4x – 5 = -15

C. -3x + 15 = 18

D. -5x – 15 = -22

9. Solve. x

8 + 6 = 32

x = ________

10. Solve.

-3x – 10 = 32

x = ________

EQUATIONS & INEQUALITIES UNIT TEST

x + 2

2x – 3

Solve the problems below. Be sure to show your thinking.


11. Solve.

16 > -8 + x

_____________________

12. Solve.

5x + 9 = 65

_____________________

13. Solve.

-3x + 12 < 18

_____________________

Match the following inequalities to the correct graph below.

14. _____

15. _____

16. _____

17. A fifteen passenger van is rented for a family vacation. The van rental is $75.00 per day, plus a $160.00 insurance fee. Which inequality could be used to find x, the number of days the car be rented if they want to spend less than $760.00 on the van rental?

A. 75.00 + 160.00x < 760.00

B. 75.00x + 160.00 > 760.00

C. 75.00 + 160.00x > 760.00

D. 75.00x + 160.00 < 760.00

18. Emily is encouraged to read more than 4 hourseach week. It takes her 45 minutes to finish her first book. She divides the remainder of the time equally amongst the other six days. What is the minimum number of minutes she should read each day?

A. x > 32.5 minutes

B. x > 40 minutes

C. x ≤ 32.5 minutes

D. x ≤ 40 minutes

19. Solve and graph the following inequality.

Solution: _____________________

Graph:

20. Solve and graph the following inequality.

Solution: _____________________

Graph:

−2.5x − 9 <1616 ≥ 6+

x

2

A. -5 > x

B. x ≤ -3.5

C. -2 < x

-5 -4 -3 -2 -1

-6 -4 -2 0 -2

-5 -4 -3 -2 -1

D. x > -5

E. -2 > x

F. -3.5 ≤ x

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