Simplify. 1.) 5(7x – 12) 2.) (–3 – 4p)(3) 3.) 4 - 2(–6y + 2)

Simplify.

1.) 5(7x – 12)

2.) (–3 – 4p)(3)

3.) 4 - 2(–6y + 2)

Warm-up 10/14/2010

Algebra 1 Chapter 3 Sections 1-5

PE: A1.1.B Solve Problems that can be represented by linear functions, equations,

and inequalities.

Equivalent: has the same value, “is equal” Inverse Operations: operations that undo

each other. Linear Equation: An equation where the

variable (or variables) are raised to the first power, do not occur in the denominator, inside a square root, or inside absolute value symbols.

Example: 3x-2=27 is a linear equation

Vocabulary

Are the following Linear Equations? Why?

x + 5 = 9 yes

x2 + 5 = 9 no

-4 + n = 2n - 6 yes

|x + 3| = 7 no

Linear or Not?

( ) distribute • Can you combine like terms on the LHS? ____ (do

it!) • Can you combine like terms on the RHS? ____ (do

it!) • If variables are on both sides, then make one go

away. • What side of the new equation is the variable on?

____ • Is there a number being added or subtracted to

THAT side? ___ (get rid of it! Do the opposite.) • Is there a number “next to” the variable? _____

(get rid of it! DIVIDE.)

Solve x - 5 = -13 for x.

Examples

Solve -8 = n - (-4)

Examples

Simplify.

1.) -5(6x – 11)

2.) (3 – 7p)(-2)

3.) 4 - 2(–7y - 2)

Entry Task 10/20/2011

Solve x – 7 = 13 for x.

Solve 3 – (-x) = 12 for x.

Exit Task

Solve using multiplication and division

1.) 2.)

3.) 4x = 12 4.)


32

x

m3

210

305

x

Classify the following numbers as Real, Irrational, Rational, Integers, whole numbers , or natural

1.) 4 2.) ¾ 3.) -2

Exit Task

Chapter 2 test Get out your math notebook Get out your knowledge folder Make sure there is at lease 1 foot between

you and your neighbor. Make sure you have a pencil, calculator and

eraser to take the quiz.

Simplify.

1.)

Solve 2.) 3.)


3

4)43(

6

5x

55

2x 86

3

1x

The usual rate for taking and projecting professional movies is 24 frames per second. Find the total number of frames in a movie that is 90 minutes long.

Exit Task

Simplify:

1.) 2.)

3.) 4.)

5.)


)3(5

6 x)4(35 xx

837 xx )2(34 xx

Simplify the following: 1.) -6(x+5) 2.) (r-3)(-4)

3.) m(m-1) 4.) (-2a)(a+3)

5.) Write an expression for the perimeter of the trapezoid shown below and simplify it


Homework Questions?

Pg. 148 #1-9, 11-35odd, due 10/21

Extra Credit Pg. 148 # 10-36 even, 57-61

Homework

Simplify:

1.) 2.)

Determine whether the given number is a solution to the equation or inequality.

3.) 8+r2 = 16; 4 4.) 2(5y-4)=14; 7.5

5.)


xx

2333

4xx )13(


Evaluate the following for x=21.) 2x+7 2.) 5x2 + 2

3.) 3[(x-2)+x] 4.) 3(x-8)x


5.) 8+r2 = 16; 2 6.) 2(5y-4)=14; 2.2


1.)

2.)

3.)

4.)

5.)

6.)

Chapter 2 test retake (again) Get out your math notebook Get out your knowledge folder Make sure there is at lease 1 foot between

you and your neighbor. Make sure you have a pencil, calculator and

eraser to take the quiz.

Equations can have zero, one or many solutions.

Equations with one solution can be worked out to equal one number.

Number of Solutions

552197 xx

If the variables cancel out and the numbers left are not equal there are no solutions

NO Solution

42 xx

If the variables cancel out and the two sides of the equal sign are equal then there are many solutions, in fact x would be all real numbers.

Many solutions

63)2(3 xx

Homework Questions?

Evaluate the following for x=51.) 2x+7 2.) 5x2 + 2

3.) 3[(x-2)+x] 4.) 3(x-8)x


5.) 8+r2 = 16; 5 6.) 2(5y-4)<14; 2

Solve.7.) 8.)


63)2(3 xx 42 xx

Objective: Solve a formula for one of its variables.

Section 3.7

The formula for the area of a rectangle is A=lw

Find a formula for l in terms of A and w.

Solving Formulas

Rewrite the equation so that x is a function of y

Rewriting an Equation in Function Form

43 yx


552197 xx

213)2(6 xx

Simplify:

1.) 2.)

3.) 4.)

Solve:

5.)

6.)

)3(5

6 x)4(35 xx

837 xx )2(34 xx


1.)

2.)

3.)

4.)

5.)

6.)

Solve using multiplication and division

1.) 2.)

3.) 4x = 12 4.)

5.) Decide if the following are functions, state the domain and range if they are.


32

x

m3

210

305

x

1234

Input Output2

4

5

Input Output1234

57

9


552197 xx

213)2(6 xx

Simplify:

1.) 2.)

3.) 4.)

Solve:

5.)

6.)

)3(5

6 x)4(35 xx

837 xx )2(34 xx

Identifying functions A relation is any set of ordered pairs. A Function is a relation where for every

input there is exactly one output.

f(x) is read “f of x” or “the value of f at x”. It Does not mean f times x

f(x) is called function notation.

Write y = 3x + 2 in function notation

Function notation f(x) is read “f of x” or “the value of f at x”. It

Does not mean f times x f(x) is called function notation.

Write y = 3x + 2 in function notation

a.) b.)

Examples

552197 xx 213)2(6 xx

a.) b.)

Examples

yy 6980 ww 6)316(4

a.) b.)

Examples

)1(23)1(4 xxx )2(310)1612(4

1 xx

Solve:

1.) 2.)


96)43(2 xxxx 414217

Homework Questions?

Quiz

When finished with Quiz quietly work on:

Agenda for today

Pg. 157#1-11, 19-250ddExtra Credit pg. 157 #12-40 even, 47=49

Solve:

1.) 2.)


16)2(4 x18538 xx

Objective: Solve problems using linear equations

Section 3.5

ExampleGAZELLE AND CHEETAH

A gazelle can run 73 feet per second for several minutes. A cheetah can run faster (88 feet per second) but can only sustain its top speed for about 20 seconds before it is worn out. How far away from the cheetah does the gazelle need to stay for it to be safe?

ExampleA pate of your school yearbook is 8 ½ inches by 11 inches. The left margin is ¾ inch and the space to the right of the pictures is 2 7/8 inches. The space between pictures is 3/16 inch. How wide can each picture be to fit three across the width of the page?

Pg. 163 #1-5

Extra Credit pg. 163 #18-21, 27

Homework

Solve:

1.) 2.)


xx 313)2(4 xx 21838

Objective: Solve problems using linear equations

Section 3.5

Pg. 163 # 6-13E.C. 14-17, 23-26

Homework

Solve:

1.) 2.)

3.) Round the following numbers to the indicated Place value.

a.) 1041, tens placeb.) -3.755, hundreds place


yy 2)4(10 5647 mm

Objective: Find exact and approximate solutions of equations that contain decimals.

Section 3.6

Three people want to share equally in the cost of a pizza. The pizza costs $12.89. How much should each person pay?

Rounding for Practicality

Solve 3.58x-37.40=0.23x=8.32. Round to the nearest hundredth.

Original equation with decimals

Pg. 169 #1-13 skip #2

E.C. 14-38 even

Homework

Solve:

1.) 2.)

3.) Round the following numbers to the indicated Place value.

a.) 1041, tens placeb.) -3.755, hundredths place


yy 3.22.4 1.54.63.45.7 mm

A=1/2bh is the formula for the area of a triangle. Solve this formula for b, the base of the triangle.

Solve 3x+5 = 20 for x


Objective: Rewrite an equation in function form.

Section 3.7 cont.

rewrite the following equations so that y is a function of x


16412 yx 20155 xy

Get out your planner and write the following homework assignment in for today:◦ Pg. 371 #17-28 due Monday

Solve:


)74(210824 aaa

Pg. 193 #1-21This is worth a quiz grade

Practice test

Documents

Simplify. 1.) 5(7x – 12) 2.) (–3 – 4p)(3) 3.) 4 - 2(–6y + 2)