A LGEBRA CHAPTER 3 Solving and Graphing Linear Inequalities.

ALGEBRA CHAPTER 3Solving and Graphing Linear Inequalities

ONE-STEP LINEAR INEQUALITIES—3.1

VOCABULARY

An equation is formed when an equal sign (=) is placed between two expressions creating a left and a right side of the equation

An equation that contains one or more variables is called an open sentence

When a variable in a single-variable equation is replaced by a number the resulting statement can be true or false

If the statement is true, the number is a solution of an equation

Substituting a number for a variable in an equation to see whether the resulting statement is true or false is called checking a possible solution

INEQUALITIES

Another type of open sentence is called an inequality.

An inequality is formed when and inequality sign is placed between two expressions

A solution to an inequality are numbers that produce a true statement when substituted for the variable in the inequality

INEQUALITY SYMBOLS

Listed below are the 4 inequality symbols and their meaning

< Less than≤ Less than or equal to> Greater than≥ Greater than or equal to

Note: We will be working with inequalities throughout this course…and you are expected to know the difference between equalities and inequalities

GRAPHS OF LINEAR INEQUALITIES

Graph (1 variable) The set of points on a number line that

represents all solutions of the inequality

GRAPHS OF LINEAR INEQUALITIES

WRITING LINEAR INEQUALITIES

Bob hopes that his next math test grade will be higher than his current average. His first three test scores were 77, 83, and 86.

Why would an inequality be best in this case?

How can we come up with this inequality?

Graph!

SOLVING ONE-STEP LINEAR INEQUALITIES

Equivalent Inequalities Two or more inequalities with exactly the same

solution

Manipulating Inequalities All of the same rules apply to inequalities as

equations*

When multiplying or dividing by a negative number, we have to switch the inequality! Less than becomes greater than, etc.

SOLVING WITH ADDITION/SUBTRACTION

SOLVING WITH MULTIPLICATION/DIVISION

WHY DO WE HAVE TO CHANGE THE SIGN?

Is there another way we can solve this?

SOLVING MULTI-STEP LINEAR INEQUALITIES—3.2

ALGEBRA CHAPTER 3 Solving and Graphing Linear

Inequalities

MULTI STEP INEQUALITIES

Treat inequalities just like you would normal, everyday equations*

*change the sign when multiplying or dividing by a negative!!

EXAMPLES:

EXAMPLE

You plan to publish an online newsletter that reports the results of snow cross competitions. You do not want your monthly costs to exceed $2370. Your fixed monthly costs are $1200. You must also pay $130 per month to each article writer. How many writers can you afford to hire in a month?

EXAMPLES: TRY THESE ON YOUR OWN!

o-4 -3-5o-4 -3-5●-4 -3-5

-4 -3-5●

1.

2.

3.

4.

Answer NowAnswer Now

1) WHICH GRAPH REPRESENTS THE CORRECT

ANSWER TO > 1k

4

2) WHEN SOLVING > -10WILL THE INEQUALITY SWITCH?

1. Yes!2. No!3. I still don’t

know!

x

3


3) WHEN SOLVINGWILL THE INEQUALITY SWITCH?

1. Yes!2. No!3. I still don’t

know!

a4

6


4) SOLVE -8P ≥ -96

1. p ≥ 12 2. p ≥ -123. p ≤ 124. p ≤ -12


o-15 -14-16o-15 -14-16●-15 -14-16

-15 -14-15●

1.

2.

3.

4.


5) SOLVE 7V < -105

CLASS WORK:

P.343 #15-37 ODD

IF YOU DO NOT FINISH IN CLASS, THEN IT BECOMES HOMEWORK!

COMPOUND INEQUALITIES—3.6

ALGEBRA CHAPTER 3 Solving and Graphing Linear

Inequalities

COMPOUND INEQUALITY

What does compound mean? Compound fracture?

So…what’s a compound inequality? An inequality consisting of two inequalities

connected by an and or an or

GRAPHING COMPOUND INEQUALITIES

Graph the following:

GRAPHING COMPOUND INEQUALITIES

Graph the following: All real numbers that are greater than or equal to

-2 and less than 3

SOLVING COMPOUND INEQUALITIES

Again….treat these like equations!

Whenever we do something to one side…

…We do it to every side!

SOLVING COMPOUND INEQUALITIES

HOMEWORK:

P.349 #12-36 EVEN

SOLVING ABSOLUTE-VALUE EQUATIONS AND INEQUALITIES—3.6 (DAY 1)

ABS. VALUE

What is Absolute Value? Distance from zero

What does that mean?

ABS. VALUE

So….an absolute value equation has how many solutions?

Is this always true?

ABS. VALUE

How do we apply this to equations?

Ex:

EXAMPLES

P.356#19-36

SOLVING ABSOLUTE-VALUE EQUATIONS AND INEQUALITIES—3.6 (DAY 2)

ABSOLUTE VALUE AND INEQUALITIES

EXAMPLES

A LGEBRA CHAPTER 3 Solving and Graphing Linear Inequalities.

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