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Chapter 1

Chapter 1. Section 3 Solving Equations. Verbal Expressions to Algebraic Expressions. Example 1: Write an algebraic expression to represent each variable expression. 7 less than a number Three times the square of a number The cube of a number increased by 4 times the same number.

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Chapter 1

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  1. Chapter 1 Section 3 Solving Equations

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

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

  4. Algebraic to Verbal • Example 2: Write a verbal sentence to represent each equation. • 10 = 12 – 2 • n + (-8) = -9 • n/6 = n2

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

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

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

  8. 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

  9. 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

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

  11. 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

  12. 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.)

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

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

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

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

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

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