# Inequalities Unit 3 Inequalities Name Period Day Started Day Completed

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```					             Unit 3

Inequalities

Name: ______________________

Period: _____________________

Day Started: _________

Day Completed: _________

Topic                                                               Book     Pages in
Title                 Essential Questions
#                                                                 Section    Packet
- What are the inequality
1      Basic Inequalities                                          3-1        2
symbols and what do they mean?

- How do you know when to flip
the inequality symbol? How do
3-2
you solve an inequality?
3-3
2      Solving Inequalities          - How do you solve an                    3-4
3-4
inequality?
3-5
- How do you graph an
inequality on a number line?

- What key words in a sentence
3-2
imply inequality?
Word problems                                            3-3
3                                    - How do you write the                   5-6
involving inequalities                                      3-4
inequality that models the word
3-5
problem?
-What is a compound inequality?
- How do you solve and graph
Compound                 compound inequalities?
4                                                                  3-6        7-8
Inequalities          - How do you write a compound
inequality that models a word
problem?

1
Topic 1: Basic Inequalities

An inequality is a __________________________ of values. The values are
compared using the following signs

<                     >                    ≤                    ≥
Less Than          Greater Than       Less Than or Equal   Greater Than or Equal
to                     to
“is less than”    “is greater than”
“is smaller than”    “is larger than”        “is at least”         “is at most”
“is more than”

Translate the following sentences to algebraic inequalities

1.   Nine more than a number is less than 15.

2. 3 less than a number is less than -6

3. A number increased by 6 is less than or equal to 4.

4. A number decreased by 13 is at most 15.

5. Twice the quantity of a number and 6 is at most 12.

2
Topic 2: Solving Inequalities

A _______________________________________ is any/all value(s) that make
the inequality _______________.

Steps for solving an inequality:
1. Solve like an equality (equation)
2. If you have to divide/multiply by a negative flip the sign.

Why do we flip the sign???

Here’s a true statement

Divide both sides by -1, do not flip signs

Is the resulting a true statement?

How do you make it true?

___________      __________       ____________________ ___________

Prove that the same is true for multiplying by a negative.

3
Solve each inequality and graph.
1) g – 5 ≥ 6                       2)
1
x ≤3                    3) 12 < 3p + 6
2

4) 7 – 2t ≤ 21                     5) 4f + 160 ≤ 500             6) -12 > -4x - 8

7)
2
x -5>7                      8) 3 < 2d – 5(d + 3)          9) 2m > 4m – 6
3

10) 9y + 3 > 4y - 7                11) 1.5x – 1.2 < 3.1x – 2.8   12) -5(y + 3) – 6 < y + 3

4
Topic 3: Word problems involving inequalities

1) Ms. Chinappi saved \$550 to go on a trip      2) Aliyah must sell at least 50 candy bars for a
over Columbus Day weekend. The cost of       school fund-raiser. She already sold 36 candy
the hotel room, including tax is \$80 per     bars. Write and solve an inequality to determine
night. Write an inequality to show the       how many more baskets Aliyah must sell for the
number of nights I could choose to stay      fund-raiser.
without going over the amount of money I
saved.                                             Know        Don’t Know
Know           Don’t Know

3) Jahmel made a budge and has at most \$16      4) Dan earns \$5.95 per hour working after
to spend on entertainment each week. So far     school. He needs at least \$215 for his holiday
this week, he spent \$7.50. Write and solve an   shopping. How many hours must he work to reach
inequality to determine how much money          his goal?
Jahmel can spend on entertainment the rest of       Know           Don’t Know
the week.
Know            Don’t Know

5
5) Jake earns \$9.85 per hour working at a        6) Members of the football boosters are planning
software company. He wants to earn at least      to sell programs at games. The cost to print the
\$300 a week. How many full hours must he         programs is \$150 plus \$0.50 per program. They
work to earn the money?                          plan to sell each program for \$2. How many
Know           Don’t Know                     programs must they sell to make a profit of at
least \$500?
Know             Don’t Know

7) Tamara has a cell phone plan that charges     8) An online music club has a one-time
\$0.07 per minute plus a monthly fee of \$19.00.   registration fee of \$13.95 and charges \$0.49 to
She budgets \$29.50 per month for total cell      buy each song. If Emma has \$50.00 to join the
phone expenses without taxes. What is the        club and buy songs, what is the maximum number
maximum number of minutes Tamara could use       of songs she can buy?
her phone each month in order to stay within
her budget?

6
Topic 4: Compound Inequalities

Compound inequality:
-    Two or more simple inequalities connected by the word ______ or ______.
-    Also in set theory (last unit), inequalities connected by ______ or ______.

Example 1) Write an inequality that represents the set of numbers described and
graph the solution.
a) All real numbers that are greater than zero and less than or equal to four.

b) All real numbers that are at most -3 or more than 0

c) All real numbers that are less than -1 or greater than 2.

d) All real numbers that are at least -2 and no more than 3.

Example 2) Solving and graphing compound inequalities (including interval notation)
a) 18 ≤ 3x ≤ 30               b) 3x + 4 > 10 and x < 5    c) 6x – 5 < 7 or 8x + 1 > 25

d) -6 < -2x + 4 or x > 6         e) -2 ≤ 3x – 8 < 10             f) (3, 5] ∩ [4, 8)

g) [-3, 2]    (1, 8]             h) (-∞, 6] ∩ [2, ∞)             i) (3, 6]   (-1, 8)

Example 3) Write the compound inequality shown by each graph.

a)

b)

7
On Your Own: Pg. 206: 17-23 odd. 24-27 30-33

Compound Inequalities Applications
1. Write inequalities that
describe the elevation of
the different regions of
Mount Rainer.

(a) Timber Region

(b) Alpine Region

(c) Glacier Region

2. Jonelle just bought a new Toyota Prius. She is estimated to get approximately
51 miles per gallon (MPG) in the city and 48 MPG on the highway. Her tank holds
12 gallons of gas. Write and graph a compound inequality representing how far
she can drive with a tank full of gas.

3. Brittany just bought a new Hummer H3. She is estimated to get approximately
14 MPG in the city and 18 MPG on the highway. Brittany has 12 gallons of gas in
her tank. Write and graph a compound inequality representing how far she can
drive with 12 gallons of gas.

8

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