ving quci ions] - Algebra 1 2 Notebook Key.pdf · Solving Multi Step Equations 3O 24 Writing Equations and Solving Oct i Review 25 Review 6oWeeks TEST 26 TEST Early Release Day Essentiam

Name" Teacher" Per:

..... ÿ,

Unit 1 Unit2 Unit 3 Unit 4 Unit 5 Unit 6 Unit 7 Unit 8 Unit 9 Unit 10

!./

/ving

[3Fq

3x-2 = 4

3X3ÿ2 = 4N

+2ÿ +2

3x = 6

3X = 6

3 3

x = 2

quci ions]

Add 2 to both sides

Divide both sides by 3

Unit 2- Solving Equations

• : 4To U¢¢e$$ ra c as:s,

Wi $ W000

#TENACITY during our practice, have...

D ! attempt all practiceD l attempt all homeworkD ! never give up when I don't understand

#iNTEGRITY as we help others with their work, maintain a...

#GO-FOR.qT attitude, continually...;J

D I always check my answers

D I correct my work, I never just copy answers

1-1 I explain answers, I never just give them

D I write down all notes, even if I'm confused

D ! remain positive about my goals

D i treat each day as a chance to reset

#ENCOURAGE each other to succeed as a team, and always...

D I offer help when I understand the material

D i push my teammates to reach their goals

D I never let my teammates give up

#REACH-OUT and ask for help when we need it!D I ask my questions during homework check

D I ask my teammates for help during practicei-I ! attend enrichment/tutorials when i need to

Unit 2- Solving Equations

Unit Camendar

MONDAYSep 15Classifying NumbersNumber Properties1-Step Equations

16TUESDAY

29

Solving Equationswith Variables on

Both Sides

Distributing first.

22

EvaluatingExpressions

WEDNESDAY17Combining Like Terms

18THURSDAY

Distributing

19FRIDAY

Solving 2 StepEquations

QUIZSolving 2-StepEquations with

Combining or

Equations Review

23

Solving Multi StepEquations

3O

24

Writing Equationsand Solving

Oct i

Review

25

Review

6oWeeks

TEST

26

TEST

Early Release Day

Essentiam Questions

:ÿ What is the best method to solve a problem?

Why is it useful to write, transform, and/or solve equations that model situations?

What is a solution and how do I show that it is reasonable?

Unit 2- Solving Equations

Critical Vocabumary°+_

+ +.

Real Numbers

® Solution

® Associative property

® Commutative property

+ _ ,

" ::i: ::0 Distributive property

® Algebra Tiles"

X2 X 1 -X2

s"

Unit 2- Solving Equations

Classifying Numbers

Rational Numbers° Any number than be written as a fraction/ratio.

rrational Numbers" Any number than ÿÿN uTÿ be written as a fraction/ratio.

Whole Numbers" Any number that can be written without a iVucCÿa¢ÿ [Jÿ"

JÿqrBoNÿ/bÿ[ÿÿC, part.ora

ntegers: Any number that can be written without a decimal/fractionalpart, but can be FÿCTIoNÿL or DÿQÿAL .

i

Let's place the following numbers" 4, -9, o, ÿ, s.;, ÿ, 1.2s, ¢ÿ,

Rational ÿLÿ/ÿ Irrational

Whole

0

Integer -Cÿ

Unit 2- Solving Equations

Number Properties

Properÿ,. Ad]dlitian Mud[tip[[cation

C.ommuCative

Associative:

Sum er p¢oÿcÿ

Distributive

of- TNe gALbLE$

ooes

Z

a+b-b+a a..b - b. a

(ÿ. b). ÿ- ÿ,. (b.c)

a(b + c) -a,b + ac

Unit 2- Solving Equations

14 ; 14

1-Step Equations

4x- 8

4

- 5 4

DDSDDS

D

! ÿ. 3 4

-ÿ Dr-3

4x- 8

X---23

Tiles Algebra Notationx+4-5

%

Unit 2- Solving Equations

o........

::or the following expressions:

Evaluating Expressions

a - 2 b--1 c-5 x--3 y-6 z--4

Examples"

3Z

2z2 + x a(xz- b)+2z

Find the volume of a rectangular p, riÿ, V- &vh, if the length is 3, theÿ:ÿ is 5, and the height is 12

z.(ÿ3÷z zJ,J4

Practice"

xy+z

3

z(-4 + b)

z

.....

Find the perimeter of a rectangular, P = 2(I + w)if the width is 8 and the length is 9.

P= 7__ ,?-_ 5

if the volume is 8 and the mass is 32.Find the density of an object, D ---,

I)- o .

3(b -x) abc + xyz

Kinetic Energy is found with the formula ½(my2). Find the Kinetic Energy for an object with mass - 4 and

velocity - 5.! ÿ I 5)ÿ ÿ'ÿ" 00) ÿ

.

Unit 2 - Solving Equations

Unit 2- Solving Equations

_

TransJating Words to Algebra

Sum DifferenceCombined

TimesProduct

ofTwice

Doub[e/Triple

Increased byPlus

***Added to

*** More than

Decreased byMinus

Subtracted from***Less than

***Fewer than

Divided byQuotient

PerHalfRatio

Plus the sum of ...

AreWill be

Twice the difference of ,.,

Minus the product of ..

Unit 2- Solving Equations

Examples:

I The product of a number and 5.......

.:":":.::::.......• <..<.:.:.:,..........

Twice the difference of a number

aÿa2 ZC - )3 more than twice a number

+3 ;( }

5x

5 times the sum of a number and 3

x+l

1 more than a number

+ÿ

5(x+ 3)2 less than one-third of a number

1/3x- 2

6 less than a number

3 subtracted from 4 times anumber -ÿ ÿ::ÿ®

2(x-2)The difference of a number and 4

2x+3

4x-3

Practice"

7 less than a number

-- . '..

Two-thirds of a number

Theÿa number and 10

- xy !%+IoTwice the difference of a numberand 5 ?ÿ,

17 subtracted from 4 times an'ÿber "- ÿ(')

{x-17

o

The difference of a number and 7

9 more than twice a numberj-------__-

2.( )

2 more than triple a number4- 3"( .... )

3x 2_

3 more than a number

Three times the sum of a numberand 1

30 less than one-half of a number

±z x -508 less than one-fifth of a number

_1_5X-$

i

Unit 2- Solving Equations

Combining Like Terms

D Must be the same ÿ and in order to "combine.

i-1 The standard is to write the combined answer starting with largest exponents first and working down.

Examples With Algebra Tiles"

!

x2 + 4x-

-2x + 7x + 1

Examples Without Algebra Tiles:

-4x + l Ox 12r ÿ + 3r -ÿ

"2_

.6

Unit 2 - Solving Equations

Application Problems"

Bob had three functions, g(x) - 2x2 + 5x - 3, p(x) - 4x - 7, and s(x) - 3x3 + 10. Find g(x) + p(x) + s(x).

-ÿo 4---ÿo-

-5-q + ÿoWrite an expression for the perimeter of the figure below:

3;x ÷ 2:

2x÷ S

Practice"

DÿDDD-10 + 3 + (-2)

--q v

5x+3x 7-x-4

W4.-(--4) - 5

f

v"

Unit 2 - Solving Equations

Write an expression for the perimeter of the rectangle below:

,. . ,

5 :ÿ-©

V,/,z -_

5x--3 x -

)<z_Z

-7

-b

÷Sbz = Z%<

Unit 2- Solving Equations

Distributing

-.-...:.:...:.:::.:::i {ÿi/i:::xa m pies:

2(x- 4)

©0

4-

Q=I i')÷QIII)+

4- ÿr

-3(x-5)

(-Ix') + [15)3,ÿ (36x + 60)

15

i

q - 5ÿ

(6 + 3y) 5

- (}sÿ. s')

30 ÿ- 159

so I2(4x-6) for x--3

Unit 2- Solving Equations

Practice"

6(4- a)

s4 +- C-bo'}

5(n + 6) (3x-5) 4

5ÿ 4- 3O

__ÿ + 5c)_J_-2(e + 7)

-ÿ(30-25y)

kÿÿ - 14J-(-2x + 5)

Zÿ -514(5z + 6) for z - -1

2

3(5 + 5x) for x- 2

//

Unit 2- Solving Equations

r

i. -i

Unit 2- Solving Equations

Solving 2 Step Equations

2x ÷

b ÿ z

i ::ÿ!ii :/xamples"

ZY, -ÿ

Ix

+ 2y- 16 Solve for ÿL

2. 2

sxÿÿ-3o

i

-y, ÿ -q

-x io

-y, - -q

Unit 2- Solving Equations

Practice"

• ,...

6x_ÿ- 37-I

I

Y,-bL

-NÿIO + 3x- 14

3xÿ=O

q

-4xÿ - -15

-q

-21- 8x +%L

- 2x+3yÿ--6 Solve for y

r

lÿy. -b:5 --%

f-I

-gxN9:-T5

5x4Jÿkÿ = -9

.5

I --1 t-7xÿ3 =-38

-55

- 4x ÿÿ=- 8

Unit 2- Solving Equations

" ::xamples"

Solving 2 Step Equations with Distributing or Combining

-2(5x- 4) =-78

tll)x ÿ- ÿsÿ

-75 - 5(-2x +1)

--75- -it)× ÿ-5-S --5

,.

2(! + w)- P

3 3

Solve for w

- #-tLZ

%

-4x+ 8 + 7x-8

i:

Unit 2- Solving Equations

Practice"

:... -. ,

÷Iÿo ÷ ZO

-10 + 7x + 2- 9ÿx

- s -ÿo- -: (b) ÿ- z -q(ÿ)

-:o- 4#-54

tLo = )< !-Io- -ÿo v"-4x + 3x- 8 =ÿ -7

- ': t

1 ?I

45 =ÿSx +5ÿx-5

= ÿ ,!4€-- t>ÿ- ;s-5

4x- 9 + 6x-: 101

[x---ÿ / Io, =:oÿ- \/

i

For a rectangle with a length equal to 3 more than its width, P-w+w+w+3+w+3. Solve forw

,¢j

%

Unit 2 - Solving Equations

'.."::ÿ:,.::xa m p les:

Solving Multi Step Equations

x + 2(3 - x) - 4

V X/ ._ I---- - kl

wÿ

Solve for hV = Iwh

]5 - -3ÿx'@- 1) + 9

Is- (ÿso xÿ, (-s o-ÿ) ÿ- q

s--s tz')ÿq1ÿ'- ko+q

3

-X-105

it

10-ÿ- ÿ ./

tÿ ÿ g(,ÿD - ÿÿs°lve f°r v

OoV- nÿ

q3 -s]

Unit 2 - Solving Equations

Practice"

d + 4(d + 6) - -1

...

b

(12x - lo) - 31

5

I- lÿ}rtÿ

%

-lO + 4(3p +_1o) - 18

8b+5

@- JOb+ gÿb

lo)

y7_4o- lobb--O

33 - 3 + sÿ'ÿ)

Solve for r

Z

Lÿ= z

Unit 2 - Solving Equations

=

Writing Equations

Examples"Oceanside Bike Rental Shop--s twelve dollarseight dollars an hour for rÿAlyÿa paid eighty-f"our clo[laÿto rentÿbike.[How many hours' ---"--ÿicÿ stÿe p-ÿyÿo

have the bike checked out?

Sandy sold halfmore. She now

of her comic books and_then bought 8has 11. oÿ many did sÿ

%

G

Benny bought five new baseball trading cards to add to his

collection. The next day his dÿjg_ate half of his collection.There are now only!hirty -seven cards left, How manycards ÿ-iL ÿB-ÿn ny_ÿtÿ- ÿ-ÿÿ

r+ wiÿh--'7 '>( 4- ÿ__M ÿ4ÿs

Suppose it takes 48 chicken fingers to feed Mr. Young's4th grade class of 20 students. How many chicken fingerswould be needed for 30 students?

,rcken

5

Unit 2- Solving Equations

Danielle wants to purchase some clothes. She has $75: Shebuys one leather iacket for $39 and 3 pair of soÿsÿ'Each

pair of socks cost the s--"-'---"ÿÿ m--ÿ pric'ÿe. D'ÿ-- eterm----]ne the p---ÿrice ofoÿÿa!r oÿ ÿ ÿ---------ÿ!

-7¢ --- 5x eÿ

On Monday, 357 students went on a trip to the zoo. All 7buses were fÿudents had to travel in cars.--ÿow

ssq ÿ-7 x 4.1--q --1, -

Benny spent half of his allowance going to the movies.He washed the famÿ car and earned 7 dollars. What is

hÿ ÿekÿv aÿowanqÿf he endÿ ;Ei, ÿ ÿoÿa,ÿ ?

it-- ÿX+- ,, .-,

5q-¢

When ringing up a customer, a cashier needs 11 secondsas well as ÿ secondÿ

ite.._om being purchasedÿwould someone

have to purchase in orÿr the transaction to take 37

seconds? .ÿ ÿÿÿ

I

,ÿq- Jx

t- 1

._

David reaÿ of a book in 50 minutes.paÿ-ÿs'ÿ'ould he be able to read in [ÿ0 miÿes?

2_% ÿÿJ

Unit 2- Solving Equations

,-:ÿ-: :.

;:ii!ii,:iiilW" x-6

Write an Ex_xpression for the Perimeter of the rectangne below:

Express,on w,thout Simplifying" £ ÿ. ÿ-ÿ

Simplify the expression by Combining Like Terms"

2×+3ÿ

if the actuam perimeter is known to be 42. write and soJve the _Equation for x:

Knowing x. what is the width? / ÿ. [What is the length?

Knowing both the width and length, what is the area? !

A- -ÿu

,.ÿ Write an .Expression for the Area of the rectangle below:

Expression without Simplifying:

3Simplify the expression by distributing" JÿLÿ- j[ÿsÿÿP

5x+ 2:,

If the actual area is known to be 66, write and solve the Equation for x:

\

We know the width is 3, what is the length?20oR

Knowing both the width and length, what is the perimeter?

O= ?ÿ + >-?_ Zs+ - Z. --b-O"' Unit 2- Solving Equations

.... J

Unit 2 -Solving Equations

!,.:ÿ)::.!::-xa m p les:

SoUving Equations with Variables on Both Sides

I---G-4 1

k : - k

' 1-5 ÿ 13

<

14

iII) -- I)

i . • I

Unit 2- Solving Equations

• .: :..

Practice"'ÿz+81 ÿ 9z-ÿ

t

1

2. I ÿ'-'"----"---

ss15

-lgÿ- 40 =ÿ Xÿ-By4 .-7.aÿ ÿ"22k+ 1ÿ v

- -\-Sn

7yi33;ÿ-4v

k Jÿ/c + 28--g g.. ÿ'}ÿ

-q

i

Unit 2- Solving Equations

Specian Cases

:,. -. •.....,...

No Solution

"X - 0"

2(3x+ 4)-x- 8

-&

5

VariableDOES NOT CANCEL,but the equation = 0

VariableCANCELS,

False Statement

"No Solution" or "NS"

2(3x + 4)-x- 5x + 1

Infinite Solutions

VariableCANCELS,

True Statement

"Infinite Solutions" or

"All Real Numbers" orllt ]]ÿ.#1

2(3x + 4)-x- 5x + 8

toÿ ÿ- ÿ-7, ÿ- ÿ'/- ÿS

When x- 0

t-

Unit 2 - Solving Equations

Unit 2- Solving Equations

Equations Review/Extra Practice

....'.:..• .. ::-!. :.: : : •

..

2 Step Equations:

5x +\6- 36

/.

Step Equations DISTRIBUTE FIRST:

6 -3'ÿ)-- 114

- 50

<r

- 6(- 4x + 9) - 66

x- IZo2.4

)/-5

- 2(- 6 + - 138

4(- 3x + 5)-- 100

q' x - %?_0!

Unit 2- Solving Equations

2 Step Equations COMBINE LIKE TERMS FIRST:

.....

5x+ 8 + 2x--69

-e -8= --7"7

7

- 5x-4 + x-- 36

3 -- 2x + 6x + 7

--q

19- 4x + 7- 3x

2 Step Equations VARIABLES ON BOTH SUDES"

_ÿ+3m

- -ÿ0

5x+3-k3x+9

Z

__ r.ÿ

Unit 2- Solving Equations

,.....-

. ..... °

• . -.

-. .... rUnit 2 - Solving Equations

!,