Chapter 1 Section 3 Solving Equations

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

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

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

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

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

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

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

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

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

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

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.)

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

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

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

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

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