Monday 12/1 Lesson 6.9Translating Inequalities

HW #6.9Weekly Review #11

due Friday 12/5Tuesday 12/2 Lesson 7.1

One Step InequalitiesAdding & Subtracting

HW #7.1

Wednesday 12/3 Lesson 7.2One Step Inequalities

Multiplying and Dividing

HW #7.2

Thursday 12/4 Lesson 7.3Solving & Graphing

Two-Step Inequalities

HW #7.3

Friday 12/5 Lesson 7.4Multi-Step Inequalities

HW #7.4

Monday 12/8 Lesson 7.5Review for TEST

HW: # 7.5Review Sheet

Tuesday 12/9 Lesson 7.6Review

HW #7.6Complete Study Guide

Wednesday 12/10 Test Unit 7 InequalitiesReview section on Integers

#7.1 Homework PracticeSolving One-Step Inequalities Adding & Subtracting

1. Define a variable and write an inequality to model the given situation.

A light bulb can be no more than 60 watts to be safely used in this light fixture.

If w is the light bulb’s wattage, which of the following inequalities models the given situation?A. w ≤ 60B. w ≥ 60C. w>60D. w<60

2. Select the correctly graphed the solutions of the inequality. x−4≤17

A.

B.

C.

D.

3. Solve the inequality x+2<3. Then graph the solutions.

What are the solutions? Select the correct choice below and fill in the answer box to complete your choice.

A. x≥ C. x<¿

B. x>¿ D. x≤

4. At school, the maximum number of students that can be in a classroom is 27. If there are 19

students signed up for an art class, how many more students can join?

What are the solutions? Select the correct choice below and fill in the answer box to

complete your choice.

A. The number of students that can join the class is less than _______.

B. The number of students that can join the class is at least _______.

C. The number of students that can join the class is at most _______.

5. Solve x−20<−11, and then graph the solutions. Use pencil and paper.

What are the solutions? Select the correct choice below and fill in the answer box to complete your choice.

A. x≥ C. x<¿

B. x>¿ D. x≤

#7.2 Homework PracticeSolving One-Step Inequalities Multiplication & Division

Show any and all work to solve the inequalities

1. You had a bag of fruit snacks that you shared with 5 friends. Each of you got at least 3 fruit

snacks. The inequality x÷ 6≥ 3 models this situation. Solve the inequality to find the number of

fruit snacks that were in the bag.

There were at least ______ fruit snacks in the bag.

2. Over the next 16 months you have to read at least 64 books. You have to read x books per month.

The inequality 16 x≥ 64 represents this situation. Solve the inequality to find the number of books

you have to read each month.

You have to read at least _______ books per month

3. Solve the inequality. Select the correct choice below and fill in the answer box to complete your

choice.

m−3

<1

A. m< C. m >

B. m ≤ D. m ≥

4. Solve the inequality 27 x≤ 135

5. One half of Paul’s flowers fit in Richard’s garden. Richard has at most 15 flowers in his garden. Write and solve the inequality to find the number of flowers in Paul’s garden.

Let x be the number of flowers in Paul’s garden. Circle your choice to complete the inequality.

12

x¿15

Solve the inequality:

Paul has at most ______ flowers in his garden.

#7.3 Homework PracticeSolving Two-Step Inequalities

Show any and all work to solve the inequalities

<

>

≥

≤

1. Which situation below does the inequality 3+6n≤ 30 represent?

A. You need to read 30 pages of a novel. You read 3 pages per minute. After how many minutes

will you have fewer than 6 pages left?

B. You need to read 30 pages of a novel. You read 6 pages per minute. After how many minutes

will you have fewer than 3 pages left?

C. You have $30 to buy your friends lunch. If each lunch costs $6 and you plan to share a $3

dessert, how many friends can you bring?

2. Three times a number plus nine is more than fifteen. Write and solve an inequality. Graph the

solutions.

Let x be the number. Which inequality below represents the solution?

A. 3 x+9≥15

B. 3 x+9≤15

C. 3 x+9>15

D. 3 x+9<15

Solve your chosen inequality. Write your solution here: __________________

Graph your solution below.

3. The width of a rectangular garden is 14 the length plus an additional 2 ft and can be no longer than

11 ft. Write an inequality to help you find the possible lengths of the garden, L. Use pencil and

paper.

A.14

L−2 ≤11

B.14

L+2≥ 11

C.14

L−2>11

D.14

L+2≤ 11

4. Solve both inequalities below. Then compare their solutions.

16

x+5≤ 9 −4 x−19 ≤−115

Compare the solutions:

A. The inequalities have no common solutions.

B. The inequalities have one common solution.

C. The inequalities have the same solutions.

D. The inequalities have some common solutions.

#7.4 Homework Practice

Solving Multi-Step Inequalities

Show any and all work to solve the inequalities 1. Use both the addition and multiplication properties of inequality to solve the inequality. Graph

the solutions on a number line.

2 (5 y−4 )>32

Solve the inequality for y. Select the correct choice below and fill in the answer box to complete your choice.

A. y<¿

B. y ≥

C. y ≤

D. y>¿

2. Graph your solutions to #1 on the number line below:

3. Solve the inequality.5 x−2 x≤ 18

4. Maria says the solutions of the inequality are y>6. Find, and correct the error in Maria’s work shown here.

3 (2 y−5 )>−216 y−15>−21

6 y>−36y>−6

What was Maria’s mistake?A. Maria multiplied instead of dividingB. Maria subtracted instead of addingC. Maria did not distribute 3 correctlyD. Maria forgot to reverse the inequality symbol.

What are the solutions of the inequality? Select the correct choice below and fill in the answer box to complete your choice.

A. y<¿

B. y ≥

C. y ≤

D. y>¿

5. Your classmate says that the solutions to the given inequality are x>−8. Look carefully at the work. Should your friend have reversed the inequality symbol?

28−3 (2−x )<−228−6+3 x<−2

22+3 x<−23 x<−24

x>−8

Choose the correct explanation.

A. Yes, because -24 is negative.B. Yes, because 3 is positiveC. No, because -24 is negativeD. No, because 3 is positive

# 7.5 Class work & HomeworkReview for Inequalities Test

1. What is the appropriate inequality symbol for the following situation? The number of people at a local theatre is more than 131.

A. ≤B. ≠C. >D. <E. ≥

2. A math tests asks the students to solve the inequality x−2>16 and then graph the solutions. Bella said the solutions are x>14. Solve the inequality correctly and graph the solutions. What error did Bella make?

________________________________________________________________________

________________________________________________________________________

3. A light bulb can be no more than 50 watts to be safely used in this light fixture.

If w is the light bulb’s wattage, which of the following inequalities models the given situation?

A. w ≤ 50B. w ≥ 50C. w<50D. w>50

4. Solve x+15 ≤19, and then graph the solutions

5. Over the next 17 months you will have to read at least 102 books. You have to read x books per month. The inequality 17 x≥ 102 represents this situation. Solve the inequality to find the number of books you have to read per month.

You have to read at least ____ books per month.

6. A teacher writes the inequality x6<12 on the board. A student solves the inequality and gets

the result x < 2. What is the correct result? What was the student’s error?

The correct result is ________________. The student’s error was __________________

_______________________________________________________________________

7. Solve the inequality. Explain how you know the direction of the inequality sign without solving the inequality.

−4 x>20

________________________________________________________________________

________________________________________________________________________

8. One half of Cindy’s flowers fit in Paul’s garden. Paul has at least 16 flowers in his garden.

Write the correct inequality for this situation and solve.

12

x¿16

The solutions are: ________________

9. Which situation below does the inequality 9.80 n+34 ≥150 represent?

A. A ticket for a concert costs $34. There is $6.80 tax and a $3 parking fee on the total order. How many tickets should you buy if you want to spend at most $150?

B. Your weekly paycheck is at least $150. You make $9.80 an hour. How many hours do you work each week if $27 is taken out for taxes and $7 is taken out for savings?

C. You need to save at least $150. You have $27 and a friend gives you $7. How many hours do you have to work if you make $9.80 an hour?

10. A restaurant manager needs to rope off a rectangular section for a private party. The length of the section must be 3.6m. The manager can use no more than 13 m of rope.

Which inequality could you use to find the possible widths of the roped off section?

A. 7.2+2 W ≤ 13B. 3.6+W ≤ 13C. 3.6+2 W ≥13D. 7.2+W ≥13

11. 4 times a number plus 12 is more than 16.

<

>

≥

≤

Let x be the number. Which inequality below represents the situation?A. 4 x+12 ≤ 16B. 4 x+12>16C. 4 x+12<16D. 4 x+12 ≥ 16

12. James and Heather Pierce are celebrating their 30th anniversary by having a reception at a local reception hall. They have budgeted $4,500 for their reception. The reception hall charges a $50 cleanup fee plus $31 per person.

Which inequality can you use to find the greatest number of people they can invite and still stay within their budget? Then solve and graph the inequality.

A. 50 n+31 ≤ 4,500B. 31 n+50 ≥ 4,500C. 31 n+50 ≤ 4,500D. 50 n+31 ≥ 4,500

13. Use both the addition and multiplication properties of inequality to solve the inequality.

2 (2 y−4 )>−20

14. A farmer harvests 22 bushels of green peppers, 29 bushels of red peppers, and 16 bushels of yellow peppers every day. The farmer wants to know how many days, d, will it take to

harvest more than 250 bushels of peppers. Which inequalities models this situation? How many days will it take to harvest more than 250 bushels of peppers?

A. 22 d+29 d+16 d<250B. 250>22 d+29 d+16 dC. 22 d−29 d−16 d>250D. 22 d+29 d+16 d>250

It will take ______ days to harvest more than 250 bushels of peppers.

15. Your classmates says that the solutions to the given inequality are x > -4. Look carefully at the work. Should your friend have reversed the inequality symbol?

24−4 (3−x )<−424−12+4 x<−4

12+4 x<−44 x<−16

x>−4

A. Yes, because -16 is negativeB. No, because -16 is negativeC. No, because 4 is positiveD. Yes, because 4 is positive

# 7.6 Study Guide for Inequalities Test Complete the answers below to use for tomorrow’s class.

Question Correct Answer Round 1 Round 21. At most, is the clue

for which inequality symbol? (<, >, ≤, ≤)

1. 2 1 0 2 1 0

2. You have to be at least 42 inches tall to ride Kingda Ka at Six Flags. How do you write this inequality?

2. If h represents height

h _________ 42

2 1 0 2 1 0

3. Graph the answers to the following inequality.

x−6>13

3. 2 1 0 2 1 0

4. Do you have to reverse the inequality symbol for this problem?Explain

−4 d≥ 36

4. 2 1 0 2 1 0

5. What are the rules for adding integers?

5. 2 1 0 2 1 0

6. In order to subtract integers, what rule must you use?

6. 2 1 0 2 1 0

7. In the problem 6 x−9>15 what would you do first to solve?

7. 2 1 0 2 1 0