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Chapter 1 Section 3 Solving Equations

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Verbal Expressions to Algebraic Expressions Example 1: Write an algebraic expression to represent each variable expression. a)7 less than a number b)Three times the square of a number c)The cube of a number increased by 4 times the same number

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Your turn: Write an algebraic expression to represent each variable expression. 1)3 more than a number 2)Six times the cube of a number 3)The square of a number decreased by the product of 5 and the number 4)Twice the difference of a number and 6

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Algebraic to Verbal Example 2: Write a verbal sentence to represent each equation. a)10 = 12 – 2 b)n + (-8) = -9 c)n/6 = n 2

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Your turn: Write a verbal sentence to represent each equation. 4) 14 + 9 = 23 5) 6 = -5 + x 6) 7y – 2 = 19

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Properties of Equality (used to solve equations) Reflexive Property a = a -7 + n = -7 + n

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Properties of Equality (used to solve equations) Symmetric Property If a = b, then b = a. If 3 = 5x – 6, then 5x – 6 = 3

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Properties of Equality (used to solve equations) Transitive Property If a = b and b = c, then a = c. If 2x + 1 = 7 and 7 = 5x – 8, then 2x + 1 = 5x – 8

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Properties of Equality (used to solve equations) Substitution Property If a = b, then a may be replaced by b and b may be replaced by a If (4 + 5)m = 18, then 9m = 18

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Example 3: Name the property illustrated by each statement. a)If 3m = 5n and 5n = 10p, then 3m = 10p b)If -11a + 2 = -3a, then -3a = -11a + 2

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Your turn: Name the property illustrated by each statement. 7) If xy = 28 and x = 7, then 7y = 28 8) a – 2.03 = a – 2.03

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More Properties… Addition & Subtraction Properties of Equality Multiplication & Division Properties of Equality (Both more or less say that an equation can be solved by adding, subtracting, multiplying, or dividing the same number from each side of the equation.)

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Example 4: Solve each equation. Check your solution. a)a + 4.39 = 76 b)-3/5 d = 18

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Your Turn: Solve each equation. Check your solution. 9) s – 5.48 = 0.02 10) 18 = ½ t

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Example 5: Solve 2(2x + 3) – 3(4x – 5) = 22

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Your Turn: 11) Solve 53 = 3(y - 2) – 2(3y - 1)

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Assignment: p.24 # 20-24 even, 27-28, 30, 32, 35-39, 42-52 even

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