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 = n2

Your turn:

• Write a verbal sentence to represent each equation.

4) 14 + 9 = 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 + 4.39 = 76

b) -3/5 d = 18

Your Turn:

• Solve each equation. Check your solution.

9) s – 5.48 = 0.02

10) 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 # 20-24 even, 27-28, 30, 32, 35-39, 42-52 even