Unit 10: Modelling and Solving One-Step Equations: ax b, Key Ideas/ Vocabulary linear equation-

Transcription

1 Name: Date: Unit 10: Modelling and Solving One-Step Equations: ax b, x a b 10.1 Modelling and Solving One-Step Equations: x ax b, b a Key Ideas/ Vocabulary linear equation- P. 76 #5 a, c, 7, 8, 1, 14, 17, 18-, Modelling and Solving Two-Step Equations: ax b c P. 85 #-11, Modelling and Solving Two-Step Equations: x b c a Distributive Property- P. 9 #8 (Solve for the variable), Modelling and Solving Two-Step Equations: a(x + b) c P. 98 #4-6, 8-14 Chapter Review P. 400 Practice Test P. 40 Math 8 Unit 10 Page 1

2 10.1 Modelling and Solving One-Step Equations: ax b, Example 1: Solve an Equation Solve each equation. Represents a positive variable Represents a negative variable Represents +1 Represents -1 a. Use Models or Diagrams x -1 x a b. Applying Opposite Operations x -1 Our goal is to x 1 isolate x! The opposite of x 1 multiplied by x is dividing by. x 4 b x-4 x -1 (-4) -1 x -1 (-4) -1 c. -t -6 n d. 7 e. 5t -5 n f. - 4 Math 8 Unit 10 Page

3 Example : Multiply to Apply the Opposite Operation For the month of January, the average afternoon temperature in Edmonton is 1 the average afternoon temperature in Yellowknife. The average afternoon temperature in Edmonton is -8 C. What is the average afternoon temperature in Yellowknife? Let t represent the temperature in Yellowknife t 4 1 t of Yellowknife (Remember of means 8 multiply) t Edmonton temperature 8 8 t The RHS LHS. So the solution is 8 correct. () t 8() t 4 t 4 t 4 The average afternoon temperature in Yellowknife is -4 C. Math 8 Unit 10 Page

4 10. Modelling and Solving Two-Step Equations: ax b c Example 1: Model with a balance scale At the mall Jessica bought some socks for $4 per pair and a soda for $. If she spent a total of $14, how many pairs of socks did she buy? The relationship between the pairs of socks and how much Jessica spent can be modelled using the equation 4s + 14 x You Try! Math 8 Unit 10 Page 4

5 xample : Model with Algebra Tiles A cow sleeps 7h a day. This amount of sleep is 1 h less than twice the amount of an elephant sleeps a day. How long does an elephant sleep? e the amount an elephant sleeps e 1 7 twice a number gives 7 one less To isolate the variable, add one positive tile to both sides Now split the number of tiles between the variables evenly. e 1 7 (4) Left Side Right Side e 4 An elephant sleeps 4 h a day. You Try! Model each equation with algebra tiles. Then, solve. a) g b) -r 7-11 Math 8 Unit 10 Page 5

6 Example Sydney borrowed $19 from her brother. The next day, she paid back $. To pay off the rest of the debt, she will give him 4/week. How many weeks will it take her to pay off the debt? w number of weeks Our goal is to isolate the variable. So you need to apply the opposite operation. 4w Subtract from both sides, to isolate the variable. 4w w 4 Divide 4 from both sides, to isolate the variable. You Try! Solve by applying the opposite operations. a) 4 + 6g -48 b) -x Math 8 Unit 10 Page 6

7 x 10. Solving Two-Step Equations: b c a 1. Solve the following problems. a) b) x x 4 1 x 4 1 (4) x 1(4) 4 4x 1(4) 4 x 48 c) k 4 6 Our goal is to isolate the variable. Apply BEDMAS backwards. - Add or subtract - Multiply or divide In this case the opposite of adding 6 is subtracting 6. The opposite of dividing by 4 is multiplying by 4. t t t () t () t 6 t 6 d) h 5 Our goal is to isolate the variable. Apply BEDMAS backwards. - Add or subtract - Multiply or divide In this case the opposite of subtracting 6 is adding 6. The opposite of dividing by is multiplying by. When you have a negative on both sides, they cancel each other out. Math 8 Unit 10 Page 7

8 Example During the NHL season, Kristian Huselius of the Calgary Flames had a total of 41 more than 1 the number of shots on goal as Jarome Iginla. If Huselius had 17 shots on goal, how many did Iginla have? 41 more means +41 Let Iginla shots s 1 1 s of Iginla s shots means s or Huselius had 17 shots means 17 s s 1 s 1 s 64 Jarome Iginla has 6 shots on goal during the season. s 64 s LHS RHS You Try! The mass of a Persian cat is typically kg less than 1 of the average mass of a border collie. The average mass of a Persian cat is 4kg. Describe how you might determine the average mass of a border collie. Math 8 Unit 10 Page 8

9 10.4 Modelling and Solving Two-Step Equations: a(x+b) c Example 1: Model With Algebra Tiles A flower garden is in the shape of a rectangle. The length of the garden is m longer than the length of the she beside it. The width of the garden is 4 m. If the area of the garden is 0 m, what is the length of the shed? What is the formula to find the area of a rectangle? A l x w 0 4(s + ) Use the distributive property. 0 4s + 8 Multiply 4 s 4s and 4 8 Use Algebra Tiles 4s when s 4() LHS RHS s The length of the shed is m. You Try! Solve by modelling the following equations. a) (g + 4) -8 b) (r ) Math 8 Unit 10 Page 9

10 Example : Solve Equations Autumn is making a square quilt with a 4-cm wide border around it. She wants the completed quilt to have a perimeter of 600 cm. What must the dimensions of Autumn`s quilt be before she adds the border? What is the perimeter? 4(s+8) 600 Method 1: Divide First 4(s+8) 600 4(s+8) s s 14 Divide by 4 to undo the multiplication. Subtract 8 to undo addition. The quilt dimensions before adding the border should be 14 x 14 cm. 4(s + 8) 600 when s 14 4(14 + 8) 600 4(150) LHS RHS Method : Use the Distributive Property First 4(s+8) 600 4s Multiply 4 by s and 8. 4s s 568 4s s 14 Subtract to undo addition. Divide by 4 to undo the multiplication. The quilt dimensions before adding the border should be 14 x 14 cm. Math 8 Unit 10 Page 10

11 You Try! Solve each equation. a) -(x ) 1 b) -0 5( + p) Math 8 Unit 10 Page 11