Solving Multi-Step Equations Day One Ms. Turk, Algebra I Unit 2-3

Check your skills! 2n - 3n -4 + 3b + 2 + 5b 9(w - 5) -10(b - 12) 3(-x + 4) 5(6 - x) = -n = 8b - 2 = 9w - 45 = -10b + 120 = -3x + 12 = 30 - 5x

Example 1: Combining Like Terms 3m + 2m + 8 = 63 Where are the like terms? Subtract 8 from both sides. Divide both sides by 5. 3m + 2m + 8 = 63 5m + 8 = 63 - 8 - 8 5m = 55 5 5 m = 11

Example 2: Combining Like Terms -5x + x - 4 = 20 Where are the like terms? Add 4 to both sides. Divide both sides by -4. -5x + x - 4 = 20 -4x - 4 = 20 + 4 + 4 - 4x = 24 - 4 - 4 x = -6

Example 3: Combining Like Terms Try this one on your own! 4y + 16 + 2y = 46 Where are the like terms? Subtract 16 from both sides. Divide both sides by 6. 4y + 16 + 2y = 46 6y + 16 = 46 - 16 - 16 6y = 30 6 6 y = 5

Example 4: Using Distributive Property Use the Distributive Property. Add 6 to both sides. Divide both sides by 3. 3(x - 2) = 12 3x - 6 = 12 + 6 + 6 3x = 18 3 3 x = 6

Example 5: Using Distributive Property Use the Distributive Property. Add 2 to both sides. Divide both sides by -6. -2(3x + 1) = 22 -6x - 2 = 22 + 2 + 2 -6x = 24 - 6 - 6 x = - 4

Example 6: Using Distributive Property Try one on your own! Use the Distributive Property. Subtract 20 from both sides. Divide both sides by -4. -4(x - 5) = 16 -4x + 20 = 16 - 20 - 20 -4x = -4 -4 -4 x = 1

Real World Problem Solving A gardener is planning a rectangular garden. His garden will be next to an existing 14-ft fence. The gardener has a total of 54 feet of fencing to build the other three sides of the garden. How long will the garden be if the width is 14 feet?

Real World Problem Solving Draw a picture! x Fence Perimeter: Add up sides. 14 x + 14 + x = 54 x

Real World Problem Solving x + 14 + x = 54 Combine like terms. Subtract 14 from both sides. Divide both sides by 2. Simplify. x + 14 + x = 54 2x + 14 = 54 - 14 - 14 2x = 40 2 2 x = 20

Real World Problem Solving Complete your picture! 20 Fence 14 20 + 14 + 20 = 54 20

Real World Problem Solving A carpenter is building a rectangular fence for a playground. One side of the playground is the wall of a building 70 feet wide. He plans to use 340 feet of fencing material. What is the length of the playground if the width is 70 ft?

Real World Problem Solving Draw a picture! x Building Perimeter: Add up sides. 70 x + 70 + x = 340 x

Real World Problem Solving x + 70 + x = 340 Combine like terms. Subtract 70 from both sides. Divide both sides by 2. Simplify. x + 70 + x = 340 2x + 70 = 340 - 70 - 70 2x = 270 2 2 x = 135

Real World Problem Solving Complete your picture! 135 Building 70 135 + 70 + 135 = 340 135

Pop Quiz. You may use your notes, a calculator, and that’s it Pop Quiz! You may use your notes, a calculator, and that’s it! No Work Shown = No Credit! 6x - 2x = 28 b. -13 = 3x - 2x - 4 c. 2(6 + y) = 24 d. -2(m + 4) = 8 e. A man is building a rectangular kennel for his dog with 30 feet of fence. One side of the kennel is against his house and does not need fencing. This side is 8 feet long. Find the dimensions of the kennel.

Workbook page 24: Exercises 1-6, 47, 50. Classwork Workbook page 24: Exercises 1-6, 47, 50.