The document provides information about inequalities: 1. It discusses the meaning of inequalities and how they differ from equations by having a range of possible solutions rather than a single solution. 2. Examples of common signs involving inequalities are presented, such as signs for minimum heights or drinking ages, and how they should be written using inequality symbols. 3. The basic rules for solving and graphing inequalities on a number line are introduced, such as using open or closed circles to represent < or ≤, and how the inequality sign must be flipped when multiplying or dividing by a negative number to maintain the relationship.

1. Monday, October 21, 2032
Today:
Warm-Up (4)
Inequalities
Class Work

2. Warm-Up Questions
1.
Order of Operations:
18 - (4 + 2 * 3) + 12
18 - (10) + 12; 8 + 12 = 20
2. (6+(9−5×3))×4
=(8+(3−40))×4; =(8+(−37))×4;
=(−29)×4; = -116
3. -13 x = - 13
10
Multiply each side by - 10
13x = 130; x = 10

3. Warm-Up Questions
4. 3|x - 3|+ 5 = - 2|x - 3| + 9
= 3|x - 3|+ 2|x - 3|= 5|x - 3|+ 5 = 9
5|x - 3|= 4; x - 3 = 4/5, -4/5
x = 4/5 + 15/5; x = 19/5
x = -4/5 + 15/5; x = 11/5

4. Introduction
to
Inequalities
Understanding
&
Solutions

5. Inequalities
 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

6. 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.

7. 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 meant to say was...
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.

8. 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
d > 21

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

10. Inequalities
Incorrect
Correct

11. 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.
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

12. 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

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

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

15. Solving Inequalities
Solve for x and Graph
1. 6x - 7 < 5
1. x < 2; Graph
2. 4(x - 2) > 20
x>3
3. x - 8 < - 6
x<2
And now 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; -2x/-2 > 4/-2; x > -2

16. Inequalities
Think about the rule for example 4 with numbers in there,
instead of variables. -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 –4 < –
2, which the number line shows is true:
If we hadn't flipped the inequality, we would have ended
up with "–4 > –2", which clearly isn't true.
When multiplying or dividing a negative coefficient,
you must flip the sign for the inequality to remain true.

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

18. Today:
Class Work:
5-1: All
5-2: All

20. Inequalities