1. 1-7 Solving Equations by Adding or Subtracting Course 3 Warm Up Warm Up Problem of the Day Problem of the Day Lesson Presentation Lesson Presentation

2. Warm Up Add, subtract, multiply, or divide. 41 4 –42 36 –8 1. 24 + 17 2. 23 – 19 3. 12 · 3 4. 6(–7) 5. 6. –250 + (–85) –64 8 –335 1-7 Solving Equations by Adding or Subtracting Course 3

3. Problem of the Day Janie’s horse refused to do 5 jumps today and cleared 14 jumps. Yesterday, the horse cleared 9 more jumps than today. He won 3 first place ribbons. How many jumps did the horse clear in the two-day jumping event? 37 1-7 Solving Equations by Adding or Subtracting Course 3

4. Learn to solve equations using addition and subtraction. 1-7 Solving Equations by Adding or Subtracting Course 3

5. Vocabulary equation inverse operation 1-7 Solving Equations by Adding or Subtracting Course 3

6. An equation is a mathematical sentence that uses an equal sign to show that two expressions have the same value. All of these are equations. 3 + 8 = 11r + 6 = 1424 = x – 7 100 2 = 50 To solve an equation that contains a variable, find the value of the variable that makes the equation true. This value of the variable is called the solution of the equation. 1-7 Solving Equations by Adding or Subtracting Course 3

7. Determine which value of x is a solution of the equation. x + 8 = 15; x = 5, 7, or 23 Additional Example 1: Determining Whether a Number is a Solution of an Equation Substitute each value for x in the equation. Substitute 5 for x. 13= 15 ?  So 5 is not solution. x + 8 = 15 ? 5 + 8 = 15 ? 1-7 Solving Equations by Adding or Subtracting Course 3

8. Determine which value of x is a solution of the equation. x + 8 = 15; x = 5, 7, or 23 Additional Example 1 Continued Substitute each value for x in the equation. Substitute 7 for x. 15= 15 ? So 7 is a solution. x + 8 = 15 ? 7 + 8 = 15 ? 1-7 Solving Equations by Adding or Subtracting Course 3

9. Determine which value of x is a solution of the equation. x + 8 = 15; x = 5, 7, or 23 Additional Example 1 Continued Substitute each value for x in the equation. Substitute 23 for x. 31= 15 ?  So 23 is not a solution. x + 8 = 15 ? 23 + 8 = 15 ? 1-7 Solving Equations by Adding or Subtracting Course 3

10. Determine which value of x is a solution of the equation. x – 4 = 13; x = 9, 27, or 17 Check It Out: Example 1 Substitute each value for x in the equation. Substitute 9 for x. 5 = 13 ?  So 9 is not a solution. x – 4 = 13 ? 9 – 4 = 13 ? 1-7 Solving Equations by Adding or Subtracting Course 3

11. Determine which value of x is a solution of the equation. x – 4 = 13; x = 9, 27, or 17 Check It Out: Example 1 Continued Substitute each value for x in the equation. Substitute 27 for x. 23 = 13 ?  So 27 is not a solution. x – 4 = 13 ? 27 – 4 = 13 ? 1-7 Solving Equations by Adding or Subtracting Course 3

12. Determine which value of x is a solution of the equation. x – 4 = 13; x = 9, 27, or 17 Check It Out: Example 1 Continued Substitute each value for x in the equation. Substitute 17 for x. 13 = 13 ? So 17 is a solution. x – 4 = 13 ? 17 – 4 = 13 ? 1-7 Solving Equations by Adding or Subtracting Course 3

13. Addition and subtraction are inverse operations, which means they “undo” each other. To solve an equation, use inverse operations to isolate the variable. This means getting the variable alone on one side of the equal sign. 1-7 Solving Equations by Adding or Subtracting Course 3

14. To solve a subtraction equation, like y  15 = 7, you would use the Addition Property of Equality. You can add the same number to both sides of an equation, and the statement will still be true. 2 + 3 = 5 + 4 2 + 7 = 9 x = y + z ADDITION PROPERTY OF EQUALITY WordsNumbersAlgebra 1-7 Solving Equations by Adding or Subtracting Course 3

15. There is a similar property for solving addition equations, like x + 9 = 11. It is called the Subtraction Property of Equality. You can subtract the same number from both sides of an equation, and the statement will still be true. 4 + 7 = 11  3 4 + 4 = 8 x = y  z z z z SUBTRACTION PROPERTY OF EQUALITY WordsNumbersAlgebra 1-7 Solving Equations by Adding or Subtracting Course 3

16. Solve. Additional Example 2A: Solving Equations Using Addition and Subtraction Properties Subtract 10 from both sides. 10 + n = 18 –10 0 + n = 8 n = 8 Identity Property of Zero: 0 + n = n. Check 10 + n = 18 ? 10 + 8 = 18 18 = 18 ? 1-7 Solving Equations by Adding or Subtracting Course 3

17. Solve. Additional Example 2B: Solving Equations Using Addition and Subtraction Properties Add 8 to both sides. p – 8 = 9 + 8 p + 0 = 17 p = 17 Identity Property of Zero: p + 0 = p. Check p – 8 = 9 ? 17 – 8 = 9 9 = 9 ? 1-7 Solving Equations by Adding or Subtracting Course 3

18. Solve. Additional Example 2C: Solving Equations Using Addition and Subtraction Properties Add 11 to both sides. 22 = y – 11 + 11 33 = y + 0 33 = y Identity Property of Zero: y + 0 = 0. Check 22 = y – 11 ? 22 = 33 – 11 22 = 22 ? 1-7 Solving Equations by Adding or Subtracting Course 3

19. Solve. Check It Out: Example 2A Subtract 15 from both sides. 15 + n = 29 –15 0 + n = 14 n = 14 Identity Property of Zero: 0 + n = n. Check 15 + n = 29 ? 10 + 14 = 29 29 = 29 ? 1-7 Solving Equations by Adding or Subtracting Course 3

20. Solve. Check It Out: Example 2B Add 6 to both sides. p – 6 = 7 + 6 p + 0 = 13 p = 13 Identity Property of Zero: p + 0 = p. Check p – 6 = 7 ? 13 – 6 = 7 7 = 7 ? 1-7 Solving Equations by Adding or Subtracting Course 3

21. Solve. Check It Out: Example 2C Add 23 to both sides. 44 = y – 23 + 23 67 = y + 0 67 = y Identity Property of Zero: y + 0 = 0. Check 44 = y – 23 ? 44 = 67 – 23 44 = 44 ? 1-7 Solving Equations by Adding or Subtracting Course 3

22. Jan and Alex are arguing over who gets to play a board game. If Jan, on the right, pulls with a force of 14 N, what force is Alex exerting on the game if the net force is 3 N? Additional Example 3: Problem Solving Application 1-7 Solving Equations by Adding or Subtracting Course 3

23. Force is measured in newtons (N). The number of newtons tells the size of the force and the sign tells the direction. Positive is to the right, and negative is to the left. Helpful Hint! 1-7 Solving Equations by Adding or Subtracting Course 3

24. Net forceAlex’s force Jan’s force = + The answer is the force that Alex, on the left is exerting on the board game. List the important information: Jan, on the right pulls with a force of 14 N. The net force is 3 N. 1 Understand the Problem Show the relationship or the information: Additional Example 3 Continued 1-7 Solving Equations by Adding or Subtracting Course 3

25. Write an equation and solve it. Let f represent Alex’s force on the board game, and use the equation model. 3 = f + 14 Subtract 14 from both sides. –11 = f Alex was exerting a force of –11 N on the board game. 2 Make a Plan Solve 3 – 14 Additional Example 3 Continued 1-7 Solving Equations by Adding or Subtracting Course 3

26. Look Back 4 Alex, the person on the left, exerts force to the left, so the force is negative. Its absolute value is less than the force the person on the right, Jan, exerts. This makes sense, since the net force is positive; thus the board game is moving to the right. Additional Example 3 Continued 1-7 Solving Equations by Adding or Subtracting Course 3

27. Frankie and Carol are playing tug of war using a rope. If Frankie, on the right, pulls with a force of 7 N, what force is Carol exerting on the game if the net force is 4 N? Check It Out: Example 3 1-7 Solving Equations by Adding or Subtracting Course 3

28. Net forceCarol’s force Frankie’s force = + The answer is the force that Carol, on the left is exerting on the rope. List the important information: Frankie, on the right pulls with a force of 7 N. The net force is 4 N. 1 Understand the Problem Show the relationship or the information: Check It Out: Example 3 Continued 1-7 Solving Equations by Adding or Subtracting Course 3

29. Write an equation and solve it. Let f represent Carol’s force on the rope, and use the equation model. 4 = f + 7 Subtract 7 from both sides. –3 = f Carol was exerting a force of -3 N on the rope. 2 Make a Plan Solve 3 – 7 1-7 Solving Equations by Adding or Subtracting Course 3 Check It Out: Example 3 Continued

30. Look Back 4 Carol, the person on the left, exerts force to the left, so the force is negative. Its absolute value is less than the force the person on the right, Frankie, exerts. This makes sense, since the net force is positive; thus the board game is moving to the right. 1-7 Solving Equations by Adding or Subtracting Course 3 Check It Out: Example 3 Continued

31. Lesson Quiz Determine which value of x is a solution of the equation. 1. x + 9 = 17; x = 6, 8, or 26 2. x – 3 = 18; x = 15, 18, or 21 Solve. 3. a + 4 = 22 4. n – 6 = 39 5. The price of your favorite cereal is now $4.25. In prior weeks the price was $3.69. Write and solve an equation to find n, the increase in the price of the cereal. 8 21 a = 18 n = 45 3.69 + n = 4.25; $0.56 1-7 Solving Equations by Adding or Subtracting Course 3