chapter 2a: equations - white plains middle school...chapter 2-4: swbat: solve equations in one...

Algebra

Foundations of Algebra

Chapter 2A: Equations

Name:______________________________

Teacher:____________________________

Pd: _______

Table of Contents

Chapter 1-6: SWBAT: Use the calculator to evaluate expressions and to compute absolute

values.

Pgs 1 - 4

Chapter 1-7: SWBAT: Identify and apply the properties of real numbers Expressions.

Pgs 5 - 9

Chapter 2-3: SWBAT: Solve equations in one variable that contain more than one operation SWBAT: Solve Equations with Rational Coefficients Pgs 10 - 15

Chapter 2-4: SWBAT: Solve equations in one variable that contain variable terms on both sides

Pgs 16 - 20

Chapter 2-5(A): SWBAT: Solve an equation in two or more variables for one of the variables

Pgs 21 - 24

Chapter 2-5(B):

SWBAT: Solve an equation in two or more variables for one of the variables

Pgs 25 - 29

1

Chapter 1-6

SWBAT: Use the calculator to evaluate expressions and to compute absolute values.

Being proficient with graphing calculator is necessary to be successful this year.

When inputting a negative value, make sure you the negative sign and NOT the subtraction sign.

When inputting a fraction, use parenthesis and use DIVISION as the fraction line.

When raising a number to an exponent use the “carrot” key

Example: 43 will be typed in as 3 ^ 4

When raising a NEGATIVE number to an exponent use parenthesis around the BASE.

Example: Evaluate 3x when 2x will be typed in as (- 2) ^ 3

Example: Evaluate - 3x when 2x will be typed in as - 2 ^ 3

Example: Evaluate - 3x when 2x will be typed in as - (- 2) ^ 3

General Rule: When uncertain always use parenthesis. The number of open brackets “ ( “

should always equal the number of closed brackets “ ) “

2

Example: Evaluate 64 )2(32

1 will be typed in as (1 / 2)(3 ^ 4)+((-2) ^ 6)

Exercise 1:

Evaluate the following expressions.

5a 4b 3

1c

Absolute Value - the _________________ a number is away from ________ on the number line

The symbol for absolute value is | | .

Distance is always ______________________

3

To use absolute value on the calculator hit: the right arrow and you will see the following screen:

Select Option 1: and type in the value inside the absolute value brackets

Example: |-3| would be typed in as abs(- 3)

Exercise 2:

1) |8|

2) |–8| = 3) –|8| = 4) –|–8| =

5) |8–12| = 6) |–4 • 3| = 7) |–30| – |–45| = 8) |–10 + 5| =

Exercise 3:

Challenge Problem

Summary

4

Exit Ticket

Chapter 1-6 Homework

Evaluate the following expressions for numbers #1 through 14.

3a 2b 3

1c

Evaluate the following expressions for numbers #15 through 20.

3x 4y

15) |x| = _______ 16) 5|y| = _________ 17) |y – x| = ___________

18) 5|x + y| = ________ 19) |2x – 2| = __________ 20) 3|y – 2| 2 =___________

5

Chapter 1-7

SWBAT: Identify and apply the properties of real numbers

Properties of Real Numbers This lesson will introduce properties that can make it easier to do mental math.

COMMUTATIVE PROPERTY FOR ADDITION AND MULTIPLICATION

Definition: You can add or multiply numbers in any _______________

- Commutative starts with “CO” which means “C____________ O____________”

- Think of the elements as “commuting” from one location to another.

Examples:

a) 4 + 2 + 5 =

b) 12 • 6 • 8 =

c) (4 + 3) + 10 =

Warm Up

6

ASSOCIATIVE PROPERTY FOR ADDITION AND MULTIPLICATION

Definition: You can add or multiply in different ________________

- Association are ________________

Examples:

a) (3 • 6) • 4 =

b) (9 + 5) + 12 =

DISTRIBUTIVE PROPERTY

Each element inside the parentheses is _____________ by the element outside the

parentheses

Examples:

a) 4( 3 + 6) =

b) 2(7 + 9) =

c) 3( y + 5) =

IDENTITIY PROPERTIES

Identity Elements and Properties for Addition and Multiplication – For both

multiplication and addition there is one number that is unique because it doesn’t change

another number when operated with. These elements are called identities.

(a) What is the identity element for addition? In other words, what number can be

added to a given number without changing that given number?

(b) What is the identity element for multiplication?

7

Practice Problems: Name the property that each exercise illustrates.

Commutative property of addition 2 + 3 = 3 + 2

Commutative property of multiplication 2 * 3 = 3 * 2

Associative property of addition (2 + 3) + 4 = 2 + (3 + 4)

Associative property of multiplication ( 2 * 3) * 4 = 2 * (3 * 4)

Distributive Property x(a + b) = ax + bx

Identity property of addition 0 + 2 = 2

Identity property of multiplication 1 * 2 = 2

1) 8(2 + 3) = 8 ( 3 + 2) ________________________________

2) 5(2 + 4x) = 10 + 20x ________________________________

3) 8(1) = 8 _____________________

4) x + 0 = x ___________________________

5) A + C = C + A ______________________

6) 3(2x + 6) = 6x + 18 ___________________________

7) 10 + 0 = 10 __________________

8) (10 * 2) * 3 = 10 * (2 * 3) ______________________________

9) 1(b) = b __________________________

10) 6 + 2 = 2 + 6 __________________________

11) (x + y) + c = x + (y + c) _______________________________

12) x(yz) = (xy)z _________________________________

8

Challenge Problem:

Summary

Exit Ticket:

9

Chapter 1-7 - Homework:

10

Chapter 2 - 3

SWBAT: Solve equations in one variable that contain more than one operation

Warm – Up

Example 1: Solving Two-Step Equations

Solve the equation. Check your solution.

A) 5t - 2 = -32 B)

Practice: Solving Two-Step Equations


1) 3x + 6 = -3 2) 39 = -3x + 3 3)

11

Example 2: Solving Equations that Contain Fractions


C)

Practice: Solving Equations that Contain Fractions


Example 3: Simplifying Before Solving Equations


D)

Solve 8x – 21 + 5x = –15.

2

5x + 4 = 10

4) 5) 6)

12

Practice: Simplifying Before Solving Equations


Example 4: Simplifying Before Solving Equations


E) -2(3 – d) = 4 F) 4(x – 2) + 2x = 40

Practice: Simplifying Before Solving Equations


7) 8) 9)

10) 11) 12)

13

Challenge Problem: Problem-Solving Application

Solve this equation for y: Solve this equation for x:

7y + 5 - 3y + 1 – 2y = 2

Summary:

Exit Ticket

(21

4)x = 4

1

2

14

Homework (Holt Page 96)

15

Extra Practice For Students Who Need More Practice

16

Chapter 2 - 4

SWBAT: Solve equations in one variable that contain variable terms on both sides

Warm – Up

Solve each equation. Check your answer.

1. 3(x – 2) = 18

2. (x + 6) - (2x + 7) - 3x = -9

Example 1: Solving Equations with Variables on Both Sides


A) -15 + 4x = - 6x + 5

Practice: Solving Two-Step Equations


17

Example 2: Simplifying Each Side Before Solving Equations


B) Solve: -2(1 - b) = -5b + 2b + 8

Practice: Simplifying Each Side Before Solving Equations


An identity is an equation that is true for all values of the variable. An equation that is an identity has

infinitely many solutions.

18

A contradiction is an equation that is not true for any value of the variable. It has no solutions.

Example 3: Solving Equations with Infinitely Many Solutions or No Solutions

Solve each.

10 – 5x + 1 = 7x + 11 – 12x. 12x – 3 + x = 5x – 4 + 8x.

Practice: Solving Equations with Infinitely Many Solutions or No Solutions

Solve the equation.

4y + 7 – y = 10 + 3y 2c + 7 + c = –14 + 3c + 21.

19



Summary:

Exit Ticket

20

Chapter 2 - 4 Homework (Holt Page 103)

27. 28.

21

Chapter 2 – 5(A)


Warm – Up

Solve each equation. Check your answer.

1. 7x + 2 = 5x + 8 2. 4(2x – 5) = 5x + 4

Example 1: Solving Literal Equations

Solve for the indicated variable.

1) d = rt for r

22

Practice: Solving Literal Equations


1) rhS 2 for h 2) wxyk for x 3) IRTP for T





4) tbxm for t 5) yxwd for w





6) bmxy for x 7) pkta for k 8) 216tvth for v

2) B = T - LC for T

3) T = p + prt for r

23



Summary:

Exit Ticket

a

b - c = d for a

24

Chapter 2 – 5(A) Homework (Holt Page 110)

25

Chapter 2 – 5(B)


Warm – Up

Solve for B:

S = 2B + Ph


Solve for y.

3x + y = 12

26


Solve for y.

1. -2x + y = 8 2) 16 = 4x + y 3) 5 = y – x


Solve for y.

6x + 2y = 10


Solve for y.

1) 4x + 2y = 16 2) 20 = 15x + 5y 3) 6x - 3y = 12

4) 8x - 2y = -14 5) -9x - 3y = -27 6) - 3y - x = -12

27


Solve for y.

4x + 6x - 3y - 2y = -25

Summary:

Exit Ticket

Solve for y.

28

Chapter 2 – 5(B) - HOMEWORK

chapter 2a: equations - white plains middle school...chapter 2-4: swbat: solve equations in one...

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