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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