~ chapter 2 ~ solving equations algebra i lesson 2-1 solving one-step equations lesson 2-2 solving...

~ Chapter 2 ~Solving

Equations

Algebra I

Lesson 2-1 Solving One-Step Equations

Lesson 2-2 Solving Two-Step Equations

Lesson 2-3 Solving Multi-Step Equations

Lesson 2-4 Equations with Variables on Both Sides

Lesson 2-5 Equations & Problem Solving

Lesson 2-6 Formulas

Lesson 2-7 Using Measures of Central Tendency

Chapter Review

Algebra I

Solving One-Step Equations Notes

Lesson 2-1

n/6 = 5 x/-3 = 18

x6 x6 x (-3) x(-3)

n = 30 x = -54

-a/5 = -20 -1/4m = 8

x(-5) x(-5) a = 100 m = -32

8/15 = 2/5a

4/3 = a

1 1/3 = a

(-4/1) (-4/1)

(5/2) (5/2)

Solving Two-Step Equations

NotesLesson 2-2

Steps for Solving Two-Step Equations

(1)Use the Addition or Subtraction Property of Equality to get the term with a variable on one side of the equation.

(2) Use the Mulitplication or Division Property of Equality to write an equivalent equation in which the variable has a coefficient of 1.

10 = m/4 + 2

-2 -2 (Step 1)

8 = m/4 (Step 2)

32 = m

(x4) (x4)


NotesLesson 2-2

7 = 2y – 3 6a + 2 = -8 x/9 – 15 = 12

Justify steps for solving equations – give reasons for each step… properties, rules, or definitions…


HomeworkLesson 2-2

Practice 2-1 & Practice 2-2

Odd problems both pages

Solving Multi-Step Equations

Practice 2-1Lesson 2-3

Solving Multi-Step Equations Practice 2-2Lesson 2-3


NotesLesson 2-3

Steps for Solving Multi-Step Equations

(1)Clear the equation of fractions & decimals.

(2) Use the distributive property if grouping symbols are present.

(3) Combine Like Terms

(4) Subtract or Add using the equality property to isolate the variable.

(5) Divide or Multiply using the equality property to solve for the variable.

Examples…

2c + c + 12 = 78 3x – 4x + 6 = -2

-2y + 5 + 5y = 14 -2(b – 4) = 12

3(k + 8) = 21 15 = -3(x – 1) + 9

Solving Multi-Step Equations Notes

Lesson 2-3

Solving an Equation that Contains Fractions

Method 1 Method 2

2x/3 + x/2 = 7 2x/3 + x/2 = 7

2/3 x + ½ x = 7 6(2x/3 + x/2) = 6(7)

4/6 x + 3/6 x = 7 4x + 3x = 42

7/6 x = 7 7x = 42

(6/7) 7/6 x = 7 (6/7) ÷7 ÷7

x = 6 x = 6

m/4 + m/2 = 5/8 2/3 x – 5/8 x = 26

Solving Multi-Step Equations Notes

Lesson 2-3

Solving an Equation that Contains Decimals

(Multiply using the equality property to remove the decimals)

0.5a + 8.75 = 13.25

Multiply both sides by?????

100(0.5a + 8.75) = 100 (13.25)

50a + 875 = 1325

50a = 450

a = 9

0.025x + 22.95 = 23.65 1.2x – 3.6 + 0.3x = 2.4


HomeworkLesson 2-3

Practice 2-3 #1-46

even

Equations with Variables on Both Sides



Cumulative Review

Lesson 2-4

Equations with Variables on Both Sides NotesLesson 2-4

Use the Addition or Subtraction Properties of Equality to get the variables on one side of the equation.

Examples

6x + 3 = 8x – 21

Subtract ?

6x + 3 = 8x – 21 (Goal is to have the variable on one side of the equation)

– 6x – 6x

3 = 2x – 21 (Solve just like 2 step equations)

+21 +21

24 = 2x

÷2 ÷2

12 = x or x = 12

Try these… 2(c – 6) = 9c + 2 7k – 4 = 5k + 16

c = -2 k = 10


NotesLesson 2-4

-36 + 2w = -8w + w

w = 4

An Identity is an equation that is true for every value of the variable. 6x = 6x is an identity.

Identities and Equations with No Solutions

10 – 8a = 2(5 – 4a)

10 – 8a = 10 – 8a

+8a +8a

10 = 10 This is always true… Identity

6m – 5 = 7m + 7 – m

6m – 5 = 6m + 7

-6m -6m

-5 = 7 Not true… No Solutions


NotesLesson 2-4

Determine if the following is an identity or an equation with no solution…

14 – (2q + 5) = -2q + 9 a – 4a = 2a + 1 – 5a

Identity No solutions

Homework - Practice 2-4 #7-38

Equations & Problem Solving



Reteaching 2-3Lesson 2-5

Solving Equations with Decimals

Equations & Problem SolvingSolving Equations with

FractionsLesson 2-5

1. 42 2. 24 3. 90 4. 30 5. 8 ¼ 6. 78

7. 5 1/9 8. 11 1/9 9. -3/4 10. -14 2/7

11. 1/2a + 8 = 24; 32 yrs 12. 3/4n – 5 = 2n; -4

13. 0 14. 21. 100 or 102 2. 1000 or 103 3. 10000 or 104

4. 0.3 5. 2.2 6. 4 7. -5.8 8. 179

9. 47.775 10. n – 0.08n = 1.38; 1.5

11. n + 0.35n = 0.675; 0.5

Equations & Problem SolvingNotesLesson 2-5


NotesLesson 2-5

Homework – Practice 2-5 even

Formulas


Formulas

NotesLesson 2-6

Literal equation – an equation involving two or more variables.

Examples – d = rt, P = 2w + 2l…

Transforming Geometric Formulas

Solve the formula for the area of a triangle for h.

A = ½ bh

Solve P = 2w + 2l for w…

Solve volume of a cylinder for h…

V = π r2h

Transforming Equations

y + 2x = 5 (solve for y)

Formulas & Measures of Central Tendency

NotesLesson 2-6 & 2-

7y – 4 = 5x + 7 solve for x

Transforming Equations Containing Only Variables

m – hp = d (solve for p)

y – b = x (solve for y) m

(solve for m)

Lesson 2-7 Using Measures of Central Tendency

Mean, Median, Mode, Range, Stem & Leaf Plot

Solving an Equation

99, 86, 76, 95, x; mean 91 3.8, 4.2, 5.3, x; mean 4.8

Homework Practice 2-6 & 2-7 every 3rd problem

Using Measures of Central Tendency


Using Measures of Central Tendency

Practice 2-6 continued

Lesson 2-7

Using Measures of Central TendencyPractice 2-7Lesson 2-7

~ Chapter 2 ~Chapter Review

Algebra I Algebra I

~ chapter 2 ~ solving equations algebra i lesson 2-1 solving one-step equations lesson 2-2 solving...

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