1. HW#2:Solving Inequalities
Wed, 2/1 SWBAT… solve inequalities using addition, subtraction, multiplication, division
Agenda
WU (5 min)
Review HW#1 (10 min)
Inequalities charts (10 min)
Solving inequalities – 8 examples (20 min)
Warm-Up:
1. Take out HW#1
2. Set up notes: Topic = Solving inequalities
HW#2:Solving Inequalities 1

2. Phrases for Inequalities
<
> ≤ ≥

3. Phrases for Inequalities
<
> ≤ ≥
less than
fewer than
greater than
more than
at most
no more than
less than or equal to
at least
no less than greater than or equal to

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

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

6. x > 4 (4, ∞ ) -2 ≤ x ≤ 5 [-2, 5] -2 < x ≤ 5 (-2, 5]
Interval Notation
<
> ≤ ≥
( )
[ ]
Examples:
x > 4
(4, ∞ )
-2 ≤ x ≤ 5
[-2, 5]
-2 < x ≤ 5
(-2, 5]

7. Always use parenthesis with Infinity
Interval Notation
<
> ≤ ≥
( )
[ ]
Examples:
x ≥ 4 or x < 1
(-∞, 1) [4, ∞)
Always use parenthesis with Infinity

8. HW#2:Solving Multi-Step Inequalities
1st, Tues, 2/7 SWBAT… solve inequalities using addition, subtraction, multiplication, division
Agenda
WU (10 min)
Review HW#1: Absolute value inequalities (10 min)
Solving inequalities – 8 examples (25 min)
Warm-Up:
Solve for n: 3.7| n | = 3.2
Solve for x: | x + 1 | = 21.3
HW#2:Solving Multi-Step Inequalities
No Solution
x = 1 or x = -3 8 8

9. Solving and Graphing Inequalities by Addition and Subtraction

10. 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.
1.) d ≥ -5 [-5, ∞)
2.) m < 30 (-∞, 30)
3.) Let x = a number
3 + x ≤ 2x (subtract n from both sides)
3 ≤ x
x ≥ 3 (3, ∞)

11. 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

12. Solving and Graphing Inequalities by Multiplication and Division

13. Very important…. <  > > < ≤  ≥ ≥  ≤
When you multiply or divide each side of an inequality by a negative number you always reverse or flip the inequality sign.
<  >
> <
≤  ≥
≥  ≤

14. RATIONALE -14 < -8 7 > 4 -14 > -8 7(-2) > 4(-2) NOT TRUE!
You must change the inequality symbol
-14 < -8

15. Ex 1: -7d ≤ 147 Ex 2: 5n ≤ -25 Ex 3: Ex 4: Ex 5:
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:
d ≥ -21 [-21, ∞)
n ≤ -5 (Do NOT change the inequality sign)
r > -49 (-49, ∞)
x > -18 (Do NOT change the inequality sign) (-18, ∞)
n < -48 (-∞, -48)

16. Solving and Graphing Multi-Step Inequalities

17. Two times the difference of a number and five is no more than eight.
Tues, 2/7
SWBAT… solve multi-step inequalities
Agenda:
Five WU problems below (15 min)
Double math courses (5 min)
Review HW#2 – multi-step inequalities (10 min)
Review Quiz (5 min)
Electra’s truck problem (10 min)
WU: Solve each inequality & write in interval notation:
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) ≤ (r – 2)
1.) x ≤ -3 (-∞, -3]
2.) n = number; 2(n – 5 ) ≤ 8; n ≤ 9 [9, ∞)
3.) Empty set
4.) All real numbers 17 17

18. 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
10th
11th
12th
*Honors or Regular Algebra
*Honors or Regular Geometry and Honors Advanced Algebra
*Honors Pre-Calculus
*AP Statistics
(college credit ≥ 4) (optional)
*AP Calculus (college credit ≥ 4)
*AP Statistics (college credit ≥ 4) (optional)

19. Electra needs to rent a truck for a day to move some furniture
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
a.) m < where m is the number of miles driven.
m < 72.00
0.87m < 42.05
m < or 48 1/3 miles 19

20. Thurs, 2/9 SWBAT… solve compound inequalities
Agenda
WU (5 min)
Solving compound inequalities – 6 examples (25 min)
Two open ended compound inequalities (10 min)
Work on HW2 or HW3 (10 min)
Warm-Up:
-(3t – 5) + 7 > 8t + 3
HW#3:Solving Compound Inequalities
1.) 20 20

21. Solving and Graphing Compound Inequalities

22. h ≥ 52 and h ≤ 72 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

23. You try! Inequalities Containing and
Solve and graph the compound inequality. Write it two different ways.
1.) -2 < x – 3 < 4
2.) -5 < 3p + 7 ≤ 22
1.) 1 < x < 7
2.) -4 < p ≤ 5

24. 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”

25. You try! Inequalities Containing or
Solve and graph the compound inequality.
5n – 1 < -16 or -3n – 1 < 8
The product of -5 and a number is greater than 35 or less than 10.
n < -3 or n > -3
-5n > 35 or -5n < 10
n < -7 or n > -2

26. OPEN ENDED 1: Write a compound inequality containing and for which the graph is the empty set. Sample answer: x ≤ -4 and x ≥ 1 OPEN ENDED 2: Create an example of a compound inequality containing or that has infinitely many solutions. Sample answer: x ≤ 5 or x ≥ 1

27. Tues, 2/ SWBAT… solve compound inequalities
Agenda
WU (10 min)
Review HW3 and HW#4 (20 min)
Solve the inequality:
1.) Solve for a: 12 – (a + 3) > 4a – (a – 1)
HW4: Solving Compound Inequalities: Chemistry & Geometry
1.) a < 2 (did you forget to flip the sign?!?  ) If not,  27

28. Chemistry The acidity of the water in a swimming pool is considered normal if the average of three pH readings is between 7.2 and The first two readings for the swimming pool are 7.4 and What possible values for the third reading p will make the average pH normal?
7.2 ≤ ( p)/3 ≤ 7.8
3(7.2) ≤ 3( p)/3 ≤ 3(7.8)
21.6 ≤ p ≤ 23.4
21.6 – 15.3 ≤ p – 15.3 ≤ 23.4 – 15.3
6.3 ≤ p ≤ 8.1
The value for the third reading must be between 6.3 and 8.1, inclusive.

29. The value for the third reading must be between 6. 3 and 8
The value for the third reading must be between 6.3 and 8.1, inclusive.

30. GEOMETRY The Triangle Inequality Theorem states that the sum of the measures of any two sides of a triangle is greater than the measure of the third side.
a.) Write and solve three inequalities to express the relationships among the measures of the sides of the triangle shown above.
b.) What are the possible lengths for the third side of the triangle?
c.) Write a compound inequality for the possible values of x. 9 x 4
a.) x + 9 > 4, x > -5
x + 4 > 9, x > 5
4 + 9 > x, x < 13
b.) 6, 8, 7, 9, 10, 11, 12
c.) 5 < x < 13