~ 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)
Solving Two-Step Equations
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…
Solving Two-Step Equations
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
Solving Multi-Step Equations
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
Solving Multi-Step Equations
HomeworkLesson 2-3
Practice 2-3 #1-46
even
Equations with Variables on Both Sides
Practice 2-3Lesson 2-4
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
Equations with Variables on Both Sides
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
Equations with Variables on Both Sides
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
Practice 2-4Lesson 2-5
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
Equations & Problem Solving
NotesLesson 2-5
Homework – Practice 2-5 even
Formulas
Practice 2-5Lesson 2-6
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
Practice 2-6Lesson 2-7
Using Measures of Central Tendency
Practice 2-6 continued
Lesson 2-7
Using Measures of Central TendencyPractice 2-7Lesson 2-7
Using Measures of Central TendencyPractice 2-7Lesson 2-7
~ Chapter 2 ~Chapter Review
Algebra I Algebra I
~ Chapter 2 ~Chapter Review
Algebra I Algebra I
~ Chapter 2 ~Chapter Review
Algebra I Algebra I
~ Chapter 2 ~Chapter Review
Algebra I Algebra I
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