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## Solving One-Step Equations

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**Solving One-Step Equations**Lesson 2 – 1**Addition and Subtraction Properties of Equalitya, b, and c**are real numbersIf a = b…**What is the solution x + 13 = 27?**x + 13 = 27 x + 13 – 13 = 27 – 13 x + 0 = 14 x = 14 Why does subtracting 13 from both sides of the original equation result in an equivalent equation? Problem 1**What is the solution of -7 = b – 3?**-7 = b – 3 -7 + 3 = b – 3 + 3 -4 = b Problem 2**What is the solution of ½ = y – (3/2)?**½ = y – (3/2) ½ + (3/2) = y – (3/2) + (3/2) 4/2 = y 2 = y Got it? 2b**Multiplication and Division Properties of Equalitya, b, and**c are real numbersIf a = b…**What is the solution of 4x = 6.4?**4x = 6.4 4x/4 = 6.4/4 1x = 1.6 x = 1.6 Problem 3**What is the solution of 10 = 15x?**10 = 15x 10/15 = 15x/15 2/3 = 1x = x Got it? 3a**What is the solution of = -9?**x/4 = -9 x/4 ∙ 4 = -9 ∙ 4 1x = -36 x = -36 Problem 4**What is the solution of x/-9 = 8?**x/-9 = 8 x/-9 ∙ -9 = 8 ∙ -9 1x = -72 x = -72 Got it? 4b**What is the solution of 4/5m = 28?**4/5m = 28 4/5m ∙ 5/4 = 28 ∙ 5/4 1m = 35 m = 35 4/5 and 5/4 are called what? Problem 5**The length of an average toucan is about two thirds of the**length of a macaw. Toucans are about 24 in. long. What is the length of an average macaw? (Toucan) = 2/3 of (Macaw) T = 2/3 ∙ M 24 = 2/3M 24 ∙ 3/2 = 2/3M ∙ 3/2 36 = M The average macaw is about 36 inches. Problem 6**Lesson 2-1 #10 – 50 evens**Homework**Solving Two – Step Equations**Lesson 2 – 2**What is the solution of 2x + 3 = 15?**2x + 3 = 15 2x + 3 – 3 = 15 – 3 2x = 12 2x/2 = 12/2 x = 6 Problem 1**You are making a bulletin board to advertise community**service opportunities in your town. You plan to use half a sheet of construction paper for each ad. You need 5 sheets of paper for a title banner. You have 18 sheets of paper. How many ads can you make? ½ a + 5 = 18 ½a + 5 – 5 = 18 – 5 ½ a = 13 ½ a ∙ 2 = 13 ∙ 2 a = 26 You can make 26 ads. Problem 2**What is the solution of (x – 7) ÷ 3 = -12?**(x – 7) ÷ 3 = -12 (x – 7) ÷ 3 ∙ 3 = -12 ∙ 3 x – 7 = -36 x – 7 + 7 = -36 + 7 x = -29 Look at page 90 to see another way to write this equation. Problem 3**Lesson 2-2 #12 – 40 evens**Homework**Solving Multi-Step Equations**Lesson 2 – 3**What is the solution of 5 = 5m – 23 + 2m?**5 = 5m – 23 + 2m 5 = 5m + 2m – 23 5 = 7m – 23 5 + 23 = 7m – 23 + 23 28 = 7m 28/7 = 7m/7 4 = m Check: 5 = 5(4) – 23 + 2(4)? Problem 1**What is the solution of (s + 4) + 2s = 67?**(s + 4) + 2s = 67 s + 4 + 2s = 67 3s + 4 = 67 3s + 4 – 4 = 67 – 4 3s = 63 s = 21 Check: (21 + 4) + 2(21) = 67? Problem 2**What is the solution of -8(2x – 1) = 36?**-8(2x – 1) = 36 -8(2x) – (-8)(1) = 36 -16x + 8 = 36 -16x + 8 – 8 = 36 – 8 -16x = 28 x = -7/4 Name one mistake that could occur when solving this equation. Problem 3**Look at page 96 for Problem 4.**Problem 4**What is the solution of 3.5 – 0.02x = 1.24?**3.5 – 0.02x = 1.24 Multiply each term by 100 to eliminate the decimals 3.5(100) – 0.02x(100) = 1.24(100) 350 – 2x = 124 350 – 350 – 2x = 124 – 350 -2x = -226 x = 113 Problem 5**Lesson 2-3 #10 – 52 evens**Homework**Solving Equations with Variables on Both Sides**Lesson 2 – 4**What is the solution of 5x + 2 = 2x + 14?**5x + 2 = 2x + 14 5x + 2 – 2x = 2x + 14 – 2x 3x + 2 = 14 3x – 2 + 2 = 14 – 2 3x = 12 x = 4 Problem 1**What is the solution of 1.5p = 1.25p + 8?**1.5p = 1.25p + 8 1.5p – 1.25p = 1.25p – 1.25p + 8 0.25p = 8 p = 32 Problem 2**What is the solution of 2(5x – 1) = 3(x + 11)?**2(5x – 1) = 3(x + 11) 10x – 2 = 3x + 33 10x – 2 + 2 = 3x + 33 + 2 10x = 3x + 35 10x – 3x = 3x – 3x + 35 7x = 35 x = 5 Problem 3**What is the solution of 10x + 12 = 2(5x + 6)?**10x + 12 = 2(5x + 6) 10x + 12 = 10x + 12 10x – 10x + 12 = 10x – 10x + 12 12 = 12 There are infinitely many solutions. Problem 4a**What is the solution of 9m – 4 = -3m + 5 + 12m?**9m – 4 = -3m + 5 + 12m 9m – 4 = 9m + 5 9m – 9m – 4 = 9m – 9m + 5 -4 = 5 -4 ≠ 5 There are no solutions. Problem 4b**Lesson 2-4 #10 – 32 evens**Homework**Literal Equations and Formulas**Lesson 2 – 5**Solve the equation 10x + 5y = 80 for y.**10x + 5y = 80 5y = 80 – 10x y = 80/5 – 10x/5 y = 16 – 2x Problem 1**What equation do you get when you solve ax – bx = c for x?**ax – bx = c x(a – b) = c x = c/(a – b) x = c (a – b) Problem 2**P = 2l + 2w**C = 2∏r A = lw A = ½ bh A = ∏r2 d = rt C = 5/9(F – 32) “Famous Formulas”**What is the radius of a circle with circumference of 64 ft?**Use 3.14 for pi. C = 2∏r 64 = 2(3.14)r 64 = 6.28r r ≈ 10.2 Problem 3**Write d = rt and solve for r.**d = rt d/t = r Problem 4**Finding Perimeter, Area and Volume**Read through page 115 – 116. Complete the exercises 1 – 6.**Ratios, Rates and Conversions**Lesson 2 – 6**You are shopping for T-shirts. Which store offers the best**deal? Store A: $25 for 2 shirts Store B: $45 for 4 shirts Store C: $30 for 3 shirts Problem 1**Convert 330 minutes into hours.**Convert 5 ft 3 in into inches. Problem 2**The CN Tower I Toronto, Canada, is about 1815 ft tall.**About how many meters tall is the tower? 1 meter ≈ 3.28 ft. Problem 3**A student ran the 50 yard dash in 5.8 seconds. At what**speed did the student run in miles per hour? Round to the nearest tenth. 1 miles = 1760 yards Problem 4**Lesson 2-6 #10 – 30 evens, 48 – 52**Homework**Solving Proportions**Lesson 2 – 7**AC**BD AD =BC Cross Multiplication**What is the solution of the proportion**7 m 8 12 7(12) = 8m 84 = 8m 10.5 = m Problem 1