~ Chapter 2 ~ Algebra I Algebra I Solving Equations 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

Solving One-Step Equations Lesson 2-1 Solving One-Step Equations Notes 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 Lesson 2-2 Solving Two-Step Equations Notes Steps for Solving Two-Step Equations 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 Lesson 2-2 Solving Two-Step Equations Notes 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 Lesson 2-2 Solving Two-Step Equations Homework Practice 2-1 & Practice 2-2 Odd problems both pages

Solving Multi-Step Equations Lesson 2-3 Solving Multi-Step Equations Practice 2-1

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

Solving Multi-Step Equations Lesson 2-3 Notes Steps for Solving Multi-Step Equations Clear the equation of fractions & decimals. Use the distributive property if grouping symbols are present. Combine Like Terms Subtract or Add using the equality property to isolate the variable. 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 Lesson 2-3 Solving Multi-Step Equations Notes 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 Lesson 2-3 Solving Multi-Step Equations Notes 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 Lesson 2-3 Solving Multi-Step Equations Homework Practice 2-3 #1-46 even

Equations with Variables on Both Sides Lesson 2-4 Equations with Variables on Both Sides Practice 2-3

Equations with Variables on Both Sides Lesson 2-4 Equations with Variables on Both Sides Cumulative Review

Equations with Variables on Both Sides Lesson 2-4 Notes 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 Lesson 2-4 Notes -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 Lesson 2-4 Notes 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 Lesson 2-5 Practice 2-4

Equations & Problem Solving Lesson 2-5 Reteaching 2-3

Equations & Problem Solving Lesson 2-5 Solving Equations with Fractions Solving Equations with Decimals 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. 2 1. 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 Solving Lesson 2-5 Notes

Equations & Problem Solving Lesson 2-5 Notes Homework – Practice 2-5 even

Formulas Lesson 2-6 Practice 2-5

Lesson 2-6 Notes Formulas 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 Lesson 2-6 & 2-7 Notes y – 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 Lesson 2-7 Practice 2-6

Using Measures of Central Tendency Lesson 2-7 Practice 2-6 continued

Using Measures of Central Tendency Lesson 2-7 Practice 2-7

Using Measures of Central Tendency Lesson 2-7 Practice 2-7

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 ~ Chapter 2 ~ Chapter Review