News/NotesWarm-Up/Review

Intro to InequalitiesClass Work**Notebooks Submitted Tomorrow

November 6, 2014

Today:

News/Notes

Yesterday’s scores: Posted @ v6math.blogspot.com

Make-Up Tests: Lunch, After School by Friday.Be sure to leave notebooks after class

tomorrow, with your name clearly visible.

Khan Academy:The first three topics for the 2nd Qtr. are due November 16. No topics this week.

Not only is this 20% of your grade, but regular, consistent completion will have a positive effect on your test scores (40%) as well.

News/Notes

1st quarter grades will not be finished until Monday at the earliest and will be posted at v6math.Also at v6 math: Variety of resources to help you through our new unit, Inequalities.

1. Link to Textbook Chapter

2. Links to videos, websites, practice quizzes

3. And, of course, our daily slideshow and links to the class work.

News/Notes

Warm-Up Section

Of Note book

Warm-Up

The product of two numbers is 30. One of the numbers is x. What is the other number?

Monday, we discussed how algebra is really a set of rules, or truths about the behavior of numbers. Where arithmetic states that 5•6 = 30, algebra represents the larger patterns and relationships of numbers such as:

Write the pattern, or relationship for the following:Two consecutive

numbers consecutive odd/even numbers A number and its

oppositeA number and its reciprocalThe sum of two numbers is 35. One of the

numbers is x. What is the other number?

Warm-Up

Warm-Up

The difference of two numbers is 45, and the smaller number is x. What is the other number?The difference of two numbers is 45, and the larger number is n. What is the other number?The larger of two consecutive even numbers is x. What is the other number?Donna is x years old. Her mother is three years more than twice as old. How old is Donna’s mother?Donna is 16 years old. How old is Donna’s mother?Donna’s now 42. Her mother is...

Write the pattern, or relationship for the following:

Lastly,

Mike has c cents, which are all dimes. How many dimes does he have?

Warm-UpWarm-UpPart II Review

Convert Fractions Decimals (Simplify)

1. = (Decimal Form)

2. .048

Find the reciprocal of the following: (Simplified)

1. 3.28 3.

3.

Warm-Up Questions

3|x - 3|+ 5 = - 2|x - 3| + 9 = 3|x - 3| + 2|x - 3|=

5|x - 3|= 4;

x = + ;

x = - + ;

5|x - 3|+ 5 = 9

x - 3 = , -

x =

x =

Part II Review

155

What’s the best form of this number to use?

Introduction

to Inequalities

Understanding&

Application

Today’s Objectives:

CCSS.Math.Content.HSA.REI.B.3Solve 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.

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

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.

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".

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

Inequalities

As far as the signs are written: Incorrect Correct

Incorrect

Inequalities

Correct

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.

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

Solving Inequalities Basic

Inequalities 1. Write the inequality shown below

x < 3

x > 0

-5 < x < 2

Inequalities

Graphing Inequalities

Draw a number line and graph the following:1. 1 <x < 8 2. -2 < x <

-13. -5 < x < 2

Solving Inequalities

Solve for x and Graph

1. 6x - 7 < 51. x < 2; Graph

x > 7 x < 2

The one difference between equations & inequalities: Solve for x and

Graph4. -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

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

Solving InequalitiesTranslating 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

Today:

Class Work:5-3: All

Inequalities

Think about the rule, except instead of variables, use a number. Let’s use (4). -2 < 4 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.

When multiplying or dividing a negative coefficient, you must flip the sign for the inequality to remain true.

Once again, The one difference between solving equations and inequalities is:

Warm-Up Questions

1. Order of Operations: 18 - (4 + 2 * 3) + 12 18 - (10) + 12; 8 + 12 = 20

2. (6+(9−5×3))×49 - 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