The document provides an introduction and overview of inequalities for a math class. It includes: 1) A discussion of the key differences between equations and inequalities, noting that inequalities can have a range of solutions rather than a single value. 2) Examples of how to write inequalities using appropriate symbols (<, >, ≤, ≥) and an explanation of open vs. closed circles on a number line. 3) Steps for solving linear inequalities, with the reminder that the inequality sign must be flipped when multiplying or dividing both sides by a negative number. 4) Practice problems for students to solve and graph inequalities on a number line.

1.  Update Grade Tracker
 Warm-Up/Review
 Intro to Inequalities
 Class Work 2.4
 **Progress Reports
Next Week

2. Grade Trackers out, pls.
1) Results from Literal Equation Test:
2) Khan Academy Topics for this Week
3) CW 2.4; Inequalities—Due BOC 12/3/15
Unfortunately, only 9 students took advantage of last week’s
amnesty offer at the Khan Academy. But those that did,
mostly turned zero’s into 100’s

3. Version 3The 5 Most Missed Questions from Our Last Test
7)29% Solve A = S(1 – DN) for N
N = A)
𝑺−𝑨
𝑺𝑫
B)
𝑺𝑫
𝑺𝑨+ 𝑫
C)
𝑺+𝑨
𝑺𝑫
D)
𝑨−𝑺
𝑺𝑫
E)
𝑺+𝑫
𝑺𝑨
Version 2
28% 10. y =
𝑫𝑪
𝑯𝑪+𝑺
Solve for C C = A)
𝑫𝑯
𝒀−𝑺𝑯
B)
𝑫𝒀
𝑯−𝑺
C)
𝒀𝑺
𝑫−𝒀𝑯
D)
𝑫𝑪
𝑯𝑪+𝑺
E)
𝑫𝑪
𝑯𝑪+𝑺

4. Version 1
25% 1) Solve for b:
A)
−𝟗𝒙
𝟑𝟎
B) 3
𝟏
𝟑
x C)
𝟏
𝟑
x D) - x E) None
A) h =
𝟑𝒌
𝟐
B)
𝟐𝒌
𝟑
C) 6
D) k E) 2k
25% 3) Solve for h:
k – 2h =
𝒌 −𝟑𝒉
𝟐
25%
5) What is the correct rearrangement of the
formula v = u + at? A) u = at – v B) a =
𝒗−𝒖
𝒕
C) t =
𝒖−𝒗
𝒂
D) t =
𝒂
𝒗−𝒖
E) t =
𝒂
𝒖−𝒗

6. At V6 math.blogspot.com: A Variety of resources
to help you through our new unit, Inequalities.
1. Link to Textbook Chapter

7. 2. Links to videos, websites, practice quizzes
3. And, of course, our daily slideshow and links to
the class work.
News/Notes

8. Introduction
to
Inequalities
Understanding
&
Application

9. CCSS.Math.Content.HSA.REI.B.3
Solve linear equations and inequalities
in one variable
Recognize and correctly apply the
mathematical symbols used with inequalities
Create & solve inequalities in one variable
Determine whether the appropriate solution
to a given problem is an equation or
inequality.

10.  The Prefix 'in' means not. Incorrect, Inflexible
 Equations which have solutions are equal to a
specific value, or number: 2x = 8 can only equal
4; no other number will satisfy this equation.
 Inequalities, however, can have many answers.
They are not equal to a specific value.
 When solving inequalities, we are solving for a
range of numbers, not just one.
 Let's look at some examples of inequalities
Inequalities

11. Inequalities
Look at, and think about, the following signs:
The problem is, none of these signs say what
they're really supposed to say. Not only that,
they are all incorrect. To be correct, they
needed to include an inequality.

12. Inequalities
Let's put this sign in mathematical terms:
Let h = the height required to use the ride. The sign
says you must be 46" tall, therefore h = 46"
According to the sign, if you're not 46" tall, you cannot
ride. But how many people are exactly 46" tall?
What they really mean to say is...
You must be at least 46" tall, or in
mathematical terms...
Your height must be equal to or
greater than 46".
This is our inequality. Our solution
is not a single number, but a range
of numbers.
h > 46".

13. Inequalities
This sign obviously refers to the drinking age. But
the sign states that even 22 year olds, or 75 year
old people cannot enter. The two words missing
here are: at least
In mathematical terms, the drinking age is:
Equal to or greater than 21
a > 21

14. Inequalities
As far as the signs are written:
Incorrect Correct

15. Incorrect
Inequalities
Correct

16. Less Than; shown with an open circle on
number line; x < -4
Less Than or equal to; shown with closed
circle on number line; x < -4
Solving Inequalities
The process of solving Inequalities is the same as
equations except for one rule(which we'll get to later),
and how inequalities are shown graphically.

17. Solving Inequalities
Greater Than; shown with an open circle on
number line; x > -4
Greater Than or equal to; shown with a
closed circle on number line; x > -4

18. Basic Inequalities
1. Write the inequality shown below
x < 3
x > 0
-5 < x < 2
Solving Inequalities

19. Inequalities
Graphing Inequalities
Draw a number line and graph the following:
1. 1 <x < 8 2. -2 < x < -1 3. -5 < x < 2

20. Solving Inequalities
Solve for x and Graph
1. 6x - 7 < 5
1. x < 2; Graph x > 7 x < 2
The one difference between equations & inequalities:
Solve for x and Graph
4. -2x < 4; When multiplying or dividing by a negative
coefficient, you must switch the sign
4. -2x < 4;
2. 4(x - 2) > 20 3. x - 8 < - 6
-2x/-2 > 4/-2; x > -2

21. Solving Inequalities
Practice Problems;
Solve & Graph on Number Line
5. x - 12 < -6
5. x - 12 < -6;
+12 +12
5. x < 6;
6. 6 - 2x > - x
+2x +2x
6 > x; x < 6

22. Solving Inequalities
Inequalities include a new set of words not usually
included with equalities. Translate, solve, then write the
inequality using the correct symbols:
x is a maximum of 10 x is at least 7
x exceeds 5 x is at most -5
x is no more
than 12
When multiplying or dividing a negative coefficient,
you must flip the sign for the inequality to remain true.

23. Today:
Class Work:
5-3: All

25. Warm-Up Questions
1. Order of Operations:
18 - (4 + 2 * 3) + 12
18 - (10) + 12; 8 + 12 = 20
2. (6+(9−5×3))×4
9 - 15 = -6; 6 + (-6) = 0 * 4 = 0
−40))×4; =(8+(−37))×4;
=(−29)×4; = -1163. -13
10
x = - 13 Multiply each side by - 10
13x = 130; x = 10

26. Inequalities
Think about the rule, except instead of variables, use a
number. Let’s use (4). -2 < 4
You know that the number four is larger than the number
negative two: 4 > -2.
Multiplying through this inequality by –1, we get 2< – 4,
which the number line clearly shows is not true:
Flipping the inequality, results in "– 4 < 2", which is true.
Once again, The one difference between solving equations
and inequalities is: