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Solving Equations by Adding or Subtracting. 1-7. Warm Up. Problem of the Day. Lesson Presentation. Course 3. Solving Equations by Adding or Subtracting. 1-7. –64 8. Course 3. Warm Up Add, subtract, multiply, or divide. 2. 23 – 19. 1. 24 + 17. 41. 4. 3. 12 · 3. 36.

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1-7

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

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

  3. Solving Equations by Adding or Subtracting 1-7 Course 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

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

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

  6. Solving Equations by Adding or Subtracting 1-7 100 = 50 2 Course 3 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 = 11 r + 6 = 14 24 = x – 7 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. Course 3

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

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

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

  10. Solving Equations by Adding or Subtracting 1-7 Course 3 Addition and subtraction are inverseoperations, 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. Course 3

  11. Solving Equations by Adding or Subtracting 1-7 Words Numbers Algebra ADDITION PROPERTY OF EQUALITY + 4 + 4 + z + z Course 3 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 x = y x = y 2 + 7 = 9 Course 3

  12. Solving Equations by Adding or Subtracting 1-7 SUBTRACTION PROPERTY OF EQUALITY Words Numbers Algebra  3  3 z z Course 3 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 x = y x = y 4 + 4 = 8 Course 3

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

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

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

  16. Solving Equations by Adding or Subtracting 1-7 Course 3 Additional Example 3: Problem Solving Application 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?

  17. Solving Equations by Adding or Subtracting 1-7 Helpful Hint! 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. Course 3

  18. Solving Equations by Adding or Subtracting 1-7 1 Understand the Problem Net force Alex’s force Jan’s force = + Course 3 Additional Example 3 Continued • 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. Show the relationship or the information:

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

  20. Solving Equations by Adding or Subtracting 1-7 4 Course 3 Additional Example 3 Continued Look Back 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.

  21. Solving Equations by Adding or Subtracting 1-7 Course 3 Check It Out: Example 3 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?

  22. Solving Equations by Adding or Subtracting 1-7 1 Understand the Problem Net force Carol’s force Frankie’s force = + Course 3 Check It Out: Example 3 Continued • 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. Show the relationship or the information:

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

  24. Solving Equations by Adding or Subtracting 1-7 4 Course 3 Check It Out: Example 3 Continued Look Back 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.

  25. Solving Equations by Adding or Subtracting 1-7 Course 3 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

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