Interval Notation _Math

Agenda
1.
WU (5 min)
2.
Review HW#1 (10 min)
3.
Inequalities charts (10 min)
4.
Solving inequalities – 8 examples (20 min)

Wed, 2/1

Warm-Up:
SWBAT…
solve inequalities using addition, subtraction, multiplication,
1. Take out HW#1
division
2. Set up notes: Topic = Solving inequalities

HW#2:Solving Inequalities


Phrases for Inequalities
<

>

≤

≥

<
less than
fewer than

Phrases for Inequalities
>
≤
greater than
more than

at most
no more than
less than or
equal to

≥
at least
no less than
greater than
or equal to


Endpoints (when graphing on a number line)
<
>
≤
≥

Endpoints (when graphing on a number line)
<
>
≤
≥
Open Circle Open Circle Closed circle Closed circle


<
( )

Interval Notation
>
≤
( )

≥

[ ]

[ ]

Examples:

x>4
(4, ∞ )
-2 ≤ x ≤ 5
[-2, 5]
-2 < x ≤ 5
(-2, 5]

0

4

-2

0

5

-2

0

5


<
( )

Interval Notation
>
≤
( )

[ ]

Examples:

x ≥ 4 or x < 1
(-∞, 1) [4, ∞)

0 1

4

Always use parenthesis with Infinity

≥
[ ]


Agenda
1.
WU (10 min)
2.
Review HW#1: Absolute value inequalities (10 min)
3.
Solving inequalities – 8 examples (25 min)

1st, Tues, 2/7

Warm-Up:
SWBAT…
solve inequalities using addition, subtraction, multiplication,
1. Solve for n: 3.7| n | + 10.6 = 3.2
division
2. Solve for x: 7.25| x + 1 | + 6.8 = 21.3

HW#2:Solving Multi-Step Inequalities


Solving and Graphing Inequalities by
Addition and Subtraction


Directions: Solve the inequality, graph
the solution on a number line.

Ex 1: d – 14 ≥ -19
Ex 2: 22 > m – 8
Ex 3: Three added to a number is no
more than twice the number.


WARNING!!!!!








(Example 2 & 3)

An equation such as x = 5 can be written as 5 = x
(because of the Symmetric Property of Equality)
You CANNOT rewrite an inequality such as 3 < x as x

<3
The inequality sign always points to the lesser value (or
it’s eating the bigger number.)
In 3 < x, the inequality points to 3, so to write the
expression with x on the left, use x > 3


Solving and Graphing Inequalities
by Multiplication and Division


Very important….
When you multiply or divide each side of an inequality by a
negative number you always reverse or flip the inequality sign.

< >
> <
≤ ≥
≥ ≤


RATIONALE
7>4

7(-2) > 4(-2)
-14 > -8

NOT TRUE!
You must change the
inequality symbol

-14 < -8


Directions: Solve the inequality, graph the
solution on a number line.
 Ex

1: -7d ≤ 147
 Ex 2: 5n ≤ -25
 Ex

3:

 Ex

4:

 Ex

5:

3
− r < 21
7
x
> −3
6
n
− >8

6


Solving and Graphing Multi-Step
Inequalities


Tues, 2/7

SWBAT… solve multi-step inequalities
Agenda:
1.
Five WU problems below (15 min)
2.
Double math courses (5 min)
3.
Review HW#2 – multi-step inequalities (10 min)
4.
Review Quiz (5 min)
5.
Electra’s truck problem (10 min)

WU: Solve each inequality & write in interval notation:
1.
2.
3.
4.

6(x – 11) – 4x ≤ -72
Two times the difference of a number and five is no more than eight.

-7(k + 4) + 11k ≥ 8k – 2(2k + 1)
2(4r + 3) ≤ 22 + 8(r – 2)


Geometry AND Honors Advanced
Algebra with Trigonometry (Algebra
II)

Infinity Math Sequence for students that take Geometry
and Honors Advanced Algebra in 10th grade:
9th

*Honors or
Regular
Algebra

10th
*Honors or Regular
Geometry and
Honors Advanced
Algebra

11th
*Honors Pre-Calculus
*AP Statistics
(college credit ≥ 4)
(optional)

12th
*AP Calculus

(college credit ≥ 4)
*AP Statistics
(college credit ≥ 4)
(optional)


Electra needs to rent a truck for a day to move some furniture. The table below shows the rates of the two truck-rental
companies near her home.

a.) Write an inequality that Electra can use to find the maximum number of miles that she can drive and spend less with

Company A than Company B. Be sure to identify your variable or variables.
b) Find the maximum number of miles that Electra can drive so that she spends less than she would for a truck rented from
Company B.

Company

Daily rate

Per mile charge

A

$29.95

$0.87

B

$72.00

$0.00


Agenda
1.
WU (5 min)
2.
Solving compound inequalities – 6 examples (25 min)
3.
Two open ended compound inequalities (10 min)
4.
Work on HW2 or HW3 (10 min)

Thurs, 2/9

SWBAT… solve compound inequalities
Warm-Up:

1.

-(3t – 5) + 7 > 8t + 3
HW#3:Solving Compound Inequalities


Solving and Graphing
Compound Inequalities


Inequalities Containing and

 To ride a roller coaster, you must be at least 52 inches tall, and your height
cannot exceed 72 inches.
 If h represents the height of the rider, we can write two inequalities to
represent this.
At least 52 inches

Cannot exceed 72 inches

h ≥ 52 and h ≤ 72




The inequalities h ≥ 52 and h ≤ 72 can be combined and written without
using “and” as 52 ≤ h ≤ 72
Graph the inequality “sandwich”

Variable is isolated


Inequalities Containing and

You try!

Solve and graph the compound inequality. Write it
two different ways.
1.) -2 < x – 3 < 4

2.) -5 < 3p + 7 ≤ 22

Inequalities Containing or


SNAKES Most snakes live where the temperature
ranges from 750 F to 900 F. Write an inequality to
represent temperatures where snakes will not thrive.
Let t = temperature
t < 75 or t > 90



Graph the inequality “torpedo”


Inequalities Containing or

You try!

Solve and graph the compound inequality.
1.

5n – 1 < -16 or -3n – 1 < 8

2.

The product of -5 and a number is greater than 35
or less than 10.