PRE-ALGEBRA

Lesson 2-5 Warm-Up

PRE-ALGEBRA 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. Solving Equations by Adding and Subtracting (2-5) x + 2 = x = x = 3

PRE-ALGEBRA How do you check to make sure the answer to an algebraic equation is correct? What is the “Subtraction Property of Equality”? 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 Substitute x for 3 5 = 5  True Statement Rule: Subtraction Property of Equality: If you subtract the same value (number) from both sides of an equation (both sides are equal), 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 2 = 2  Solving Equations by Adding and Subtracting (2-5)

PRE-ALGEBRA 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 = = 10  Example: Solve c – 12 = 43 c – 12 = 43Given Use the Addition Property of Equality to isolate the variable (get the c by itself) c + 0 = 55 Simplify c = 55 Identity Property of Addition Solving Equations by Adding and Subtracting (2-5)

PRE-ALGEBRA Solve y + 5 = 13. y + 5 = 13 y = 8Simplify. Check: y + 5 = 13 (8) Replace y with = 13 y = 8Identity Property of Addition. Solving Equations by Adding or Subtracting LESSON 2-5 Additional Examples Inverse Property of Addition. + 0

PRE-ALGEBRA 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. target numberWordsplusis250number to buy =number to buy.xLet Equation 327+x250= Solving Equations by Adding or Subtracting LESSON 2-5 Additional Examples

PRE-ALGEBRA (continued) 327 = x Larissa needs to buy 77 more books. 327 = x + 250Use the Commutative Property of Addition. – 250 – 250Use the Inverse Property to isolate the x. 77 = x Simplify. Check: Is the answer reasonable? 250 plus the number of books bought should be a total collection of = (77) Solving Equations by Adding or Subtracting LESSON 2-5 Additional Examples = 327

PRE-ALGEBRA Solve c – 23 = – 40. c – 23 = – Add 23 to each side to isolate the c. c = –17Simplify. Solving Equations by Adding or Subtracting LESSON 2-5 Additional Examples + 0 c = –17Identity Property of Addition

PRE-ALGEBRA Marcy’s CD player cost $115 less than her DVD player. Her CD player cost $78. How much did her DVD player cost? Use the Inverse Property to isolate the t. 193 = tSimplify. Marcy’s DVD player cost $193. cost of CD player$115cost of DVD playerWordsless thanwas t=cost of the DVD player.Let t 115 Equation78=– 78 = t – 115 Write an equation. Solving Equations by Adding or Subtracting LESSON 2-5 Additional Examples + 0

PRE-ALGEBRA Solve each equation. 1.y + 8 = f – 21 = – = g – (–36) 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 4–6 31 Lesson Quiz Solving Equations by Adding or Subtracting LESSON 2-5