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Chapter 3 Lesson 3 Solving Equations by Adding or Subtracting pgs. 110-114

Chapter 3 Lesson 3 Solving Equations by Adding or Subtracting pgs. 110-114. What you will learn: Solve equations by using the Subtraction Property of Equality Solve equations by using the Addition Property of Equality. Vocabulary. Inverse operations (110): “undo” each other

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Chapter 3 Lesson 3 Solving Equations by Adding or Subtracting pgs. 110-114

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  1. Chapter 3 Lesson 3Solving Equations by Adding or Subtractingpgs. 110-114 What you will learn: Solve equations by using the Subtraction Property of Equality Solve equations by using the Addition Property of Equality

  2. Vocabulary Inverse operations (110): “undo” each other Ex) x + 4 to undo the addition of 4, you would subtract 4 x + 4 = 7 Remember: x + 4- 4= 7- 4 What ever you do to one x + 0 = 3side of the equation, you x = 3have to do to the other side Equivalent equations (111): two equations that equal the same Concept check: Which integer would you subtract from each side of x + 7 = 20 to solve the equation? 7 Concept check: Are x + 4 = 15 and x = 4 equivalent equations? No, the solution of x + 4 = 15 is 11, not 4

  3. Key Concept: Subtraction Property of Equality (110): Words: If you subtract the same number from each side of an equation, the two sides remain equal. Symbols: For any numbers a, b, and c, if a = b, then a-c = b-c Examples: 5 = 5 x + 2 = 3 5 - 3 = 5 - 3 x + 2 - 2 = 3 - 2 2 = 2 x = 1 You try! Check: Substitute 9 for m 9 + 6 = 15 15 = 15  x + 5 = -3 x + 5- 5= -3- 5 m + 6 = 15 x = -8 m + 6- 6= 15- 6 m = 9 Check: -8 + 5 = -3 -3 = -3

  4. Graph the Solutions of an Equation: Graph the solution of 16 + x = 14 Step 1: Solve for x x + 16 = 14 Commutative Property of Addition x + 16- 16 = 14 -16 Subtract 16 from both sides x = -2 Simplify The solution is -2. To graph the solution, draw a dot at -2 on a number line.  -3 -2 -1 0 1 2 3

  5. Key Concept: Addition Property of Equality: Words: If you add the same number to each side of an equation, the two sides remain equal. Symbols: For any numbers a, b, and c, if a = b, then a+c = b+c Examples: 6 = 6 x2 = 5 6+3= 6 + 3 x - 2 + 2 = 5 + 2 9=9 x = 7 You try! 84 = s - 34 Check: Sub 15 for r 15 - 5 = 10 10 = 10 r - 5 = 10 84 + 34= s - 34+ 34 r - 5+ 5= 10+ 5 118 = s r = 15 Check: 84 = 118-34 84 = 84

  6. Use an Equation to Solve a Problem: In the 2000 presidential election, Indiana had 12 electoral votes. That was 20 votes fewer than the number of electoral votes in Texas. Write and solve an equation to find the number of electoral votes in Texas. 12 = x - 20   Indiana’s votes 20 fewer than Texas’ votes 12 = x - 20 12+ 20 = x - 20+ 20 32 = x Texas has 32 electoral votes.

  7. Check: Practice: y + 49 = 26 q - 8 = 16 -13 + k = -2 u - 11 = -14 • 23 + 49 = 26 • 26 = 26 y + 49 - 49 = 26 - 49 y = -23 24 - 8 = 16 16 = 16 q - 8 + 8 = 16 + 8 q = 24 -13 + 11 = -2 -2 = -2 -13 + 13 + k = -2 + 13 k = 11 -3 - 11 = -14 -14 = -14 u - 11 + 11 = -14 + 11 u = -3

  8. Homework Take a practice sheet by the door! Look at the problems in the book! Use the book’s internet site! Extra practice on pg. 729!

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