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Algebra 1

Unit 4 – Inequalities

Monday Tuesday Wednesday Thursday Friday

Nov 17 A Day 18 B Day 19 A Day 20 B Day 21 A Day

Elaboration Day – Unit 3 Test – CBA #3

Solving One

Variable

Inequalities

-distributive

property

24 A Day 25 B Day 26 A Day 27 B Day 28 A Day

Thanksgiving Break

Dec 1 B Day 2 A Day 3 B Day 4 A Day 5 B Day

Solving One

Variable

Inequalities

-distributive

property

Solving One Variable Inequalities

-Variables on both Sides


-applications

-writing

Quiz – Solving Inequalities

8 A Day 9 B Day 10 A Day 11 B Day 12 A Day

Graphing Linear Inequalities – 2

variables

-is (x,y) a solution?

Retest – CBA #3

Writing and Solving Linear

Inequalities – 2 variables

-situations with inequalities

-writing

Quiz – Graphing Inequalities

Systems of

Linear

Inequalities

-graphing not

writing

15 B Day 16 A Day 17 B Day 18 A Day 19 B Day

Systems of

Linear

Inequalities

-graphing not

writing

Elaboration Day

Test – CBA #4

1

TOE THE LINE

RECALL: IS LESS THAN <

IS GREATER THAN >

OPERATION WALKER A INEQUALITY

SYMBOL WALKER B

START -1 1

ADD 2

SUBTRACT 3

MULTIPLY BY -2

ADD 1

MULTIPLY BY -1

ADD 5

DIVIDE BY 2

SUBTRACT 3

MULTIPLY BY -2

MULTIPLY BY 3

SUBTRACT 1

ADD 3

DIVIDE BY -2

Identify the operations that resulted in a switch of the inequality. What

conclusion can you draw?

3

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4


Solve and graph each inequality. Determine whether -2 is a solution for each inequality.

1. 3x – 7 ≥ 26 2. 16x + 3 + 4x < 103

Write the inequality for each scenario.

3. The spoons in the drawer are more than 20. Inequality:

4. There can be no more than 5 people on the team. Inequality:

5. The height of the building exceeds 75 stories. Inequality:

6. The number of hotdogs I have has to be less than 10. Inequality:

Write an inequality for each situation. Then solve for the variable.

7. The Reese family budgeted $2750 for vacation. Their budget consists of $550 for travel

and $125 per day. What is the maximum number of days the family can stay on

vacation?

8. Megan rents a car for a weekly fee of $132 plus $0.12 per mile. How far can she travel if

she budgets to spend at most $240?

9. An amusement park charges $6 for admission and $0.75 for each ride. Suppose you go

to the park with $20. What is the maximum number of rides you can go on?

10. Mayra is paid $180 a week plus a commission of $25 on each television she sells. How

many must she sell to make at least $450 a week?

Name Date

5

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WARM-UP #_____

Match solution to its graph.

7

Explain – Solving Inequalities with Variables on Both Sides

Solve and graph each inequality.

1. 2(7n – 1) ≥ 3(5 – n)

2. 4(1 – 3n) – 14 > 4(2n + 3) – 9n

3. -2x + 6 > 2(4 – x)

4. -18x + 7x + 2 ≥ 24 – 11x – 22

5. R & G Catering specializes in catering wedding receptions. They charge $550 for

setting up the buffet and an additional $6.50 per guest. Mr. and Mrs. Henderson

want to spend less than $1200 on their daughter’s wedding reception. Write an

inequality in terms of the number of guests that they can invite to the wedding

reception.

Independent variable: Dependent variable:

Inequality: Can 100 guests be invited? YES or NO

Circle one: CONTINUOUS or DISCRETE

Reasonable Domain: Reasonable Range:

8

One Variable Inequalities Name: _________________________________ Period: _____

Solve the following inequalities and graph the solution on the number line.

Inequality # Line Solution Check answer with

Substitution

Check answer with #

Line Solution

Is it a Solution?

x + 1 ≤≤≤≤ −−−−4

Does x = -6 make a true

statement?

x + 1 ≤≤≤≤ −−−−4

YES or NO

Is -6 in the shaded

area?

YES or NO

Is -6 a solution to this

inequality?

YES or NO

3x −−−− 9 >>>> 18

Does x = 9 make a true

statement?

3x −−−− 9 >>>> 18

YES or NO

Is 9 in the shaded

area?

YES or NO

Is a solution to this

inequality?

YES or NO

−−−−3y −−−− 7 <<<< 23

Does y = 0 make a true

statement?

−−−−3y −−−− 7 <<<< 23

YES or NO

Is 0 in the shaded

area?

YES or NO

Is 0 a solution to this

inequality?

YES or NO

−−−−5b + 4 ≥≥≥≥ 19 – 5b

Does b = 5 make a true

statement?

−−−−5b + 4 ≥≥≥≥ 19 – 5b

YES or NO

Is 5 in the shaded

area?

YES or NO


inequality?

YES or NO

10 ≤≤≤≤ 2x −−−− 12


statement?

10 ≤≤≤≤ 2x −−−− 12

YES or NO

Is 12 in the shaded

area?

YES or NO

Is 12 a solution to

this inequality?

YES or NO

3t >>>> −−−−9

Does t = -2 make a true

statement?

3t >>>> −−−−9

YES or NO

Is -2 in the shaded

area?

YES or NO


inequality?

YES or NO

5(x −−−− 2) >>>> 20


statement?

5(x −−−− 2) >>>> 20

YES or NO

Is 0 in the shaded

area?

YES or NO


inequality?

YES or NO

11

3(b + 1) ≤≤≤≤ 15 + 3b

Does b = -6 make a true

statement?

3(b + 1) ≤≤≤≤ 15 + 3b

YES or NO

Is -6 in the shaded

area?

YES or NO


inequality?

YES or NO

4y + 5 ≥≥≥≥ y + 26

Does y = -5 make a true

statement?

4y + 5 ≥≥≥≥ y + 26

YES or NO

Is -5 in the shaded

area?

YES or NO


inequality?

YES or NO

6y + 7 ≥≥≥≥ 2y + 27

Does y = 5 make a true

statement?

6y + 7 ≥≥≥≥ 2y + 27

YES or NO

Is 5 in the shaded

area?

YES or NO


inequality?

YES or NO

11. Lyle wants to build a rectangular dog pen with a

length that is 12 feet more than the width. Lyle can

afford no more than 560 feet of fence. Write and

solve an inequality to show that the perimeter of

the dog pen can be no more than 560 feet.

Independent variable: _______________

Dependent variable: _______________

Inequality solution: _______________

Can the length be 140 feet? YES or NO


Reasonable Domain: _______________

Reasonable Range: _______________

12. R & G Catering specializes in catering wedding

receptions. They charge $550 for setting up the

buffet and an additional $6.50 per guest. Mr. and

Mrs. Henderson want to spend less than $1200 on

their daughter’s wedding reception. Write an

inequality in terms of the number of guests, g that

they can invite to the wedding reception.




Can 100 guests be invited? YES or NO




13. Anthony is carpeting several rooms in his home.

The carpet costs $15 per square yard plus $200 for

installation. He can afford to spend at most $3000.

Write an inequality to represent how many square

yards of carpet Anthony can afford.



Inequality solution: _______________ (Mixed fraction!)

Can he afford 186 ¾ yd2 of carpet? YES or NO




15. Jeff’s car averages 18 miles per gallon of gasoline.

Write an inequality that could be used to find the

least number of gallons of gasoline that he will need

if he travels more than 450 miles.


Will 24.5 gallons be enough for his travels? YES or NO


12

Inequality Stations

Fill in the table for each situation.

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13

Inequality Stations

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14

Solving Inequality Situations

Fill out the table for each situation.

Sit

ua

tio

n

1. A summer camp needs a

boat and a motor. A local

charity will donate the money

if the camp spends less than

$3000 on

both. The

camp decides

to buy a boat

for $2065.

How much can be spent on the

motor in order for the charity

to pay for both?

2. A restaurant is purchasing

bread for tonight’s dinner rush.

The bread cost $1.30 per loaf

and there is a delivery fee of

$20. The restaurant only has

$267 to spend on the bread.

3. A crate for shipping lemons

weighs 6kg when empty. A

lemon weighs about 0.2 kg. In

order to ship economically, the

crate with lemons must weigh

at least 45 kg. How many

lemons should be put in the

crates?

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4. Which is the graph of the solution set of 5 – (2x + 3) ≤ –6x + 2(x – 1)?

Name Date

15

Linear Inequalities in 2-variables Notes

Find a solution to the following inequality:

y ≥ x + 3

Next, find 6 more solutions to the inequality above

( , ) ( , ) ( , )

( , ) ( , ) ( , )

Now, graph the equation y = x + 3 on the plane below

(notice how this looks kind of like the inequality above)

Lastly, plot each solution to the inequality on the same graph

above.

Therefore, where are all the solutions to the inequality?

If every solution is ___________ the line, then what would be a

good way to ‘show’ every solution to the inequality?

Graph the inequality 2 2y x

Name:_______________________

What is a solution?

A solution is any value(s) that

creates a ________ statement.

How can you find additional

solutions to the inequality?

________ and check the value(s) in

the inequality.

How is an equation different

from an inequality?

An equation relates _____ quantities

using an ____________ sign.

An inequality relates two quantities

using _______________ signs.

Are the points ‘on the line’

solutions to 3y x ?

Where are the solutions to

2 2y x in relation to the line?

Are the points on the line a

solution the inequality?

17

Given the following inequalities, in relation to the line, where are the solutions to the inequality?

3y x 1

22

y x

Circle One: Above or Below? Above or Below?

Therefore, what generalizations can you make about the difference between the following signs ?

If y x , the solutions to the inequality will be _________________ the line.

If y x , the solutions to the inequality will be _________________ the line.

Are the points on the line solutions to the inequalities? (check yes or no)

3y x 1

22

y x

Yes Yes

No No

What is the difference between y or y (regards to points on the line) ?

If y x , then the points on the line ______ _______ solutions.

If y x , then the points on the line ________ solutions.

How do you think we should ‘show’ that the points on the line are not solutions?

If the inequality is “also equal to”, then the line should be ____________.

If the inequality is not “also equal to”, then the line should be ____________.

Complete the table using your new knowledge. Only true if y is on the left side of the sign.

y y y y Shading (above or

below?)

Line (solid or

dashed?)

Points on line

(solutions or not

solutions)

18

Match the graph to the correct number. Record the

letter of the graph on the blank.

1. y < 2x 2. -5x + y > 5

3. y > 4x 4. y + 3 < 5x

5. 4

3x – 4 < y 6. -3y < -2x + 6

7. y > 5

2−x 8. x – y ≥ 2

9. -y > 1 10. y < 5x + 2

11. 3x + y > 0 12. -5y > -15 – x

13. y < 3 14. -5 > -5x – y

15. y > -2x + 6 16. y < 3x – 5

17. 3x – 5y > 5 18. y > 1

19. x + y > 1 20. x – 2y < -6

19

4.3.3 Assignment – Solving 2-variable Inequalities

https://sites.google.com/site/friscohsalgebra1/

Graph the following inequalities and determine if the point given is in the solution.

1. 2x + y < − 1

m = ________ b = ______

line ________ shade _______

Is the point (2, 2) in the solution? _______

Is the point (-3,-4) in the solution? _______

2. 15x + 5y > 10

m = ________ b = ______

line ________ shade _______

Is the point (0, −4) in the solution? ______

3. x − 2y ≥ −8

m = ________ b = ______

line ________ shade _______

Is the point (−3, 5) in the solution? ______

Is the point (−3, 5) in the solution? ______

4. 3x + 4y < 20

m = ________ b = ______

line ________ shade _______

Is the point (1, −5) in the solution? ______

21



Write the inequality of each graph below. Then

determine if the point given is in the solution.

5. m = ________ b = ______

line ________ shade _______

Inequality ____________________

Is the point (4, 0) in the solution set? ____

6. m = ________ b = ______

line ________ shade _______

Inequality ____________________

Is the point (6, 4) in the solution? ______

7. m = ________ b = ______

line ________ shade _______

Inequality ____________________

Is the point (2, 5) in the solution set? ____

8. m = ________ b = ______

line ________ shade _______

Inequality ____________________

Is the point (−5, −2) in the solution? _____

x

y

O 2

2

x

y

O 2

2

x

y

O 2

2

x

y

O 2

2

22



Wealthy Walt is planning to take his family on a trip during the winter break. Walt worked at Wendy’s during the

summer and saved $400 from his earnings and put it into a savings account. Starting the first week of school, he

added $25 to his savings every week. Walt has decided that he wants to take his family to Wally World but needs

to have some idea of a budget. He estimates the trip to cost $880.

9. Write an inequality to represent the amount of money, M, that Walt needs and the number of weeks, w,

he has been saving.

___________________________

10. Graph this inequality. Be sure to label the axes appropriately.

11. How much money has Walt saved after 12 weeks? If the budget is $880, Is it enough to take his family on

the trip? Why or why not?

12. What does the coordinate (5, 525) mean in relation to Walt’s problem?

13. Walt knows that he has 18 weeks to save before Winter Break begins. Will he have enough money to

take his family on the Wally World trip if the trip costs $880? Write and solve the inequality to support

your conclusion.

23



Write an inequality to represent each scenario. Then, graph the inequalities and label each axis.

14. Really weird Wanda collects bubble gum wrappers. She has 125 in her collection and decides to add 36

wrappers to her collection each week. Write an inequality to represent the amount of wrappers, x,

Wanda has if she wants to save at least Rhonda’s amount, y. Then solve the inequality.

__________________________

15. Gigantic Gene weighs 350 pounds. He goes on a diet and loses 20 pounds each month. Write an

inequality to represent Gene’s weight, w, after m months.

__________________________

16. Fisherman Fred began his fishing trip with 150 worms to use as bait. On average, Fred uses 18 worms an

hour to catch fish. Write an inequality to represent the number of worms remaining, w with respect to

the number of hours, h, Fred has fished.

__________________________

24

Practice – Review Inequalities pp 414-417 Name _________________________________________ Date ____________________ Period _____________

Match each inequality with its graph. Check the shading on the calculator.

5. Determine which ordered pairs are solutions to the inequality (circle them):

1y x

A (0, 0) B (2, 0) C (5, 4) D (1, 3)

Graph each inequality.

6. 2x

7. 3 12y

________1. 1

22

y x

________2. 2

23

y x

________3. 2

23

y x

________4. 1

22

y x

A. B.

C. D.

25

8. y x

9. 4 2x y

10. 2 5 10x y

11. 6 2 2x y

12. Given the graph, answer the following questions.

A. m = _________ b: ___________

B. Inequality: __________________________________

C. Solution Point: ___________ Not a solution Point: __________

D. x-intercept: _____________ y-intercept: ______________

26

Linear Applications Stations

Fill in the table for each situation.

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2

4

6

8

10

12

14

1 2 3 4 5 6 7 8 9 10

2

4

6

8

10

12

14

1 2 3 4 5 6 7 8 9 10

2

4

6

8

10

12

14

1 2 3 4 5

2

4

6

27

Linear Applications Stations

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1

2

3

4

5

6

1 2 3 4 5

1

2

3

4

5

6

7

1 2 3 4 5

1

2

3

4

5

6

1 2 3 4 5 6 7 8 9 10

1

2

3

4

5

6

7

8

9

10

28

Situations Involving Inequalities

Identify the variables and write the inequality for each situation.

1. Allen can spend at most $30 on party supplies. Cupcakes cost $2 each and sodas cost

$1.50 each.

x = y = Inequality:

2. An electronic store makes $125 profit on every DVD player it sells and $100 on every CD

player it sells. The store owner wants to make a profit of at least $500 a day selling DVD

players and CD players.

x = y = Inequality:

3. A local boys club made less than $500 selling raffle tickets. Tickets for a new car costs

$125 and tickets for a motorcycle costs $100.

x = y = Inequality:

4. Beverly is serving hamburgers and hotdogs at her cookout. Hamburger meat costs $3

per pound and hotdogs cost $2 per pound. Beverly wants to make sure she has enough

food. Beverly wants to spend at least $30.

x = y = Inequality:

Identify the variables, write the inequality, solve for y, and then graph (be sure to label each

axis). Identify 3 possible solutions.

5. Linda works at a pharmacy for $15 an hour. She also babysits for $10 an hour. Linda

needs to earn at least $90 per week.

x = y = Inequality:

Name Date

29

6. Sandy makes $40 profit on every dozen cupcakes that she sells and $80 profit for every

cake that she sells. Sandy wants to make more than $320.

x = y = Inequality:

7. Gloria is starting her own company making teddy bears. She has at most 200 pounds of

stuffing. It takes 20 pounds of stuffing to make a large bear and 10 pounds of stuffing

for a small bear.

x = y = Inequality:

30

Explain: Solving Systems of Inequalities

1. State which points are solutions to the system of inequalities graphed below.

2. Is (2, -3) a solution of the system of inequalities 8 ≥ 2x – y and 2y < –4x – 2?

Solve each by graphing. Then name one point that lies in the solution area.

3. y ≥ 2x 4. 2y + x < 6 5. y > x

x ≥ –1 3x – y > 4 x – y ≥ 3

-7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7

-7

-6

-5

-4

-3

-2

-1

1

2

3

4

5

6

7

x

y

-7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7

-7

-6

-5

-4

-3

-2

-1

1

2

3

4

5

6

7

x

y

-7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7

-7

-6

-5

-4

-3

-2

-1

1

2

3

4

5

6

7

x

y

Yes or No

A. (0, 0) ___________

B. (-3, 0) ___________

C. (-1, -5) ___________

D. (1, -2) ___________

E. (-4, 3) ___________

F. (-4, 0) ___________

31

Explain: Solving Systems of Inequalities

Write a system of inequalities for the graphs below.

6. 7.

Inequalities

_________________________

_________________________

Inequalities

_________________________

_________________________

32

Evaluate – Solving Systems of Inequalities

To Solve by Graphing Inequalities:

• Graph each part of the system all on one graph.

• Shade appropriately for both inequalities.

< or ≤ : Shade BELOW > or < : DOTTED Line

> or ≥ : Shade ABOVE ≥ or ≤ : SOLID Line

Solve each system of inequalities by graphing.

1. 3x + 4y > –4 2. y < x – 1 3. x – y < –1

x + 2y < 2 y ≤ 2x + 1 x – y > –3

-7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7

-7

-6

-5

-4

-3

-2

-1

1

2

3

4

5

6

7

x

y

-7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7

-7

-6

-5

-4

-3

-2

-1

1

2

3

4

5

6

7

x

y

-7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7

-7

-6

-5

-4

-3

-2

-1

1

2

3

4

5

6

7

x

y

4. y ≤ –x + 3 5. x > –4

y ≤ x + 3 y ≤ –1

-7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7

-7

-6

-5

-4

-3

-2

-1

1

2

3

4

5

6

7

x

y

-7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7

-7

-6

-5

-4

-3

-2

-1

1

2

3

4

5

6

7

x

y

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Evaluate – Solving Systems of Inequalities

6. Identify which points are solutions to the system of inequalities graphed below.

7. Is (-3, 6) a solution of the system of inequalities 3y ≥ –6x – 9 and 6 ≤ 3x + y?

Write a system of inequalities for the graphs below.

8. 9.

Yes or No

A. (0, 0) __________

B. (2, 2) __________

C. (-1, 4) __________

D. (4, 1) __________

E. (-3.5, -1.5) __________

Inequalities

__________________________

__________________________

Inequalities

__________________________

__________________________

34

Review – Inequalities

1. Your club team is selling candles for $10 each and coupon books for $5 each. In order to

make a profit from this fundraiser, your club has to make at least $1000 in sales.

a. Identify the variables and write an inequality.

x = y = inequality:

b. Solve for y.

2. Solve and graph the inequality. -2(x – 12) > 50

3. Is (-2, 4) a solution to the inequality -2x + 5y < 24?

4. Find the solution to the inequality system: y < x

y ≥ 3x + 1

5. Steven wants to join a sports club to get tickets to sporting events at a discounted price.

He has to pay an initial $200 fee. He can then get tickets for $50 each. Write an

inequality to show how many tickets he can buy if he can spend no more than $950.

6. Is -4 a solution to the inequality 8 + 4x > -10?

Name Date

35

7. Solve and graph the inequality.

4(1 – 3x) – 14 > 4(2x + 3) – 9x

8. Solve and graph the inequality. 8x – 3 < 2y + 3

9. Solve and graph the inequality. 10 – ⅓ x ≥ 12

10. Four less than a number is more than 15. Write an inequality and find the number.

11. What is the smallest possible integer that will be a solution to two more than six times a

number is greater than 140?

12. A hot air balloon is spotted 200 feet in the air. It is descending at a rate of 15 feet per

minute. About how many minutes will it take until it is able to reach the landing

platform that is 10 feet off the ground?

36

13. Find the solution to the inequality system: 2x – 3y ≥ 9

4x + 4y > 8

14. Write an inequality that is represented by

the graph below.

15. The graph of -2x – y = 6 is shown below.

Which point is not a solution to the

inequality -2x – y < 6?

A. (0, 0)

B. (0, -6)

C. (0, 3)

D. (3, 0)

37

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