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PRE-ALGEBRA Lesson 2-5 Warm-Up PRE-ALGEBRA Solving Equations by Adding and Subtracting (2-5) How do you solve an algebraic expression? To solve an algebraic expression, you need to isolate the variable (get the variable alone or by itself) on one side of the equal sign. To isolate the variable (letter), you need to work backwards, or “undo” numbers from the variable side by doing their inverse operations (operations which “undo” each other, or cancel each other out). Example: x + 2 = 5 We can use a balanced scale to model this. If we took two of the “1” weights from each side, we would isolate the “x” weight and both sides would remain balanced, so x = 3. x+2 = 5 - 2 -2 x+0 = 3 PRE-ALGEBRA Solving Equations by Adding and Subtracting (2-5) How do you check to make sure the answer to an algebraic equation is correct? To check an algebraic equation, substitute (replace) the letter in the original equation with the answer and simplify. If both sides are equal (in other words, the substitution makes the equation a true statement), the answer is correct. Example: Check x + 2 = 5 for x = 3 (3) + 2 = 5 5=5 Substitute x for 3 True Statement What is the Rule: Subtraction Property of Equality: If you subtract the same value “Subtraction Property (number) from both sides of an equation (both sides are equal), the two of Equality”? sides of the equal sign remain equal. If a = b, then a – c = b – c Example: If 2 •3 = 6, then 2 •3 – 4 = 6 – 4 2 = 2 PRE-ALGEBRA Solving Equations by Adding and Subtracting (2-5) What is the “Addition Property of Equality”? Rule: Addition Property of Equality: If you add the same value (number) to both sides of an equation, the two sides of the equal sign remain equal. If a = b, then a + c = b + c Example: If 2 •3 = 6, then 2 •3 + 4 = 6 + 4 10 Example: Solve c – 12 = 43 c – 12 = 43 +12 +12 c + 0 = 55 c = 55 = 10 Given Use the Addition Property of Equality to isolate the variable (get the c by itself) Simplify Identity Property of Addition PRE-ALGEBRA Solving Equations by Adding or Subtracting LESSON 2-5 Additional Examples Solve y + 5 = 13. y + 5 = 13 -5 -5 Inverse Property of Addition. y+0 = 8 Simplify. y Identity Property of Addition. = 8 Check: y + 5 = 13 (8) + 5 13 13 Replace y with 8. = 13 PRE-ALGEBRA Solving Equations by Adding or Subtracting LESSON 2-5 Additional Examples Larissa wants to increase the number of books in her collection to 327 books. She has 250 books now. Find the number of books she needs to buy. Words target number Let Equation x 327 is 250 plus number to buy = number to buy. = 250 + x PRE-ALGEBRA Solving Equations by Adding or Subtracting LESSON 2-5 Additional Examples (continued) 327 = 250 + x 327 = x + 250 – 250 – 250 77 = x + 0 Use the Commutative Property of Addition. Use the Inverse Property to isolate the x. Simplify. Larissa needs to buy 77 more books. Check: Is the answer reasonable? 250 plus the number of books bought should be a total collection of 327. 327 = 250 + (77) 327 = 327 PRE-ALGEBRA Solving Equations by Adding or Subtracting LESSON 2-5 Additional Examples Solve c – 23 = – 40. c – 23 = – 40 + 23 + 23 c + 0 = –17 Add 23 to each side to isolate the c. Identity Simplify.Property of Addition PRE-ALGEBRA Solving Equations by Adding or Subtracting LESSON 2-5 Additional Examples Marcy’s CD player cost $115 less than her DVD player. Her CD player cost $78. How much did her DVD player cost? Words cost of CD player Let t Equation 78 was = + 115 193 = t + less than cost of DVD player = cost of the DVD player. 78 = t – 115 + 115 $115 0 t – 115 Write an equation. Use the Inverse Property to isolate the t. Simplify. Marcy’s DVD player cost $193. PRE-ALGEBRA Solving Equations by Adding or Subtracting LESSON 2-5 Lesson Quiz Solve each equation. 1. y + 8 = 12 4 2. 7 + f – 21 = –20 –6 3. 67 = g – (–36) 31 4. Ricky rides his bike 12 miles every day. He stops after 7 miles to rest. How much farther does he have to ride? 5 mi PRE-ALGEBRA