Download Deductive Reasoning - Old Saybrook Public Schools

November 22, 2016
Solve each equation. Show
1.) 3(x + 5) - 7 = 20
all steps.
2.) x + 5
=4
6
3.) 5x - 7 = 2x + 11
Deductive Reasoning
Deductive reasoning - uses facts, rules, definitions, or
properties to reach logical conclusions from given
statements.
Ex. A gym only allows people with memberships to
work out at the gym.
John is working out at the gym,so John must have a
membership.
November 22, 2016
Determine whether the conclusion is based on inductive or
deductive reasoning.
1.) Every time Austin wears his lucky socks to a soccer game he
scores a goal. He is wearing his socks today, so he concludes
that he will score a goal.
2.) If Kevin is late making his car payment, he will be charged a
late fee. Kevin is late making his car payment, so he concludes
that he will be charged a late fee.
A deductive argument is a logical chain of statements
linking the given information to the statement you are
trying to prove.
Each statement is justified with a reason: a definition,
property, postulate, or theorem.
November 22, 2016
2-6 Algebraic Proof
Properties of real numbers
Addition Property of Equality
If a = b, then
a+c=b+c
Subtraction Property of Equality
If a = b, then
a-c=b-c
Multiplication Property of Equality
If a = b, then
a c=b c
Division Property of Equality
If a = b, then
a=b
c c
Reflexive Property of Equality
a=a
Symmetric Property of Equality
If a = b, then
b=a
Transitive Property of Equality
If a = b and
b = c, then
a=c
Substitution Property of Equality
Ex: If a = b and a+5 = c
then b + 5 = c
Distributive Property
If a = b, then
a may be replaced by b in
any expression
a(b + c) = ab + ac
November 22, 2016
Given: 3(x + 5) - 7 = 20, Prove x = 4
Statements
Given:
x+5 4
=
6
Statements
Reasons
Prove: x = 19
Reasons
November 22, 2016
Given: 2(x + 7) - 8 = 10x + 10, Prove: x = -1/2
Statements
Reasons
State the property that justifies each statement
1.) If
x + 17 = 53
then
2.) If
then
3.) If
then
x + 17 - 17 = 53 - 17
Prop: ____________
x = 76
76 = x
Prop: ____________
x + 4 = 9x and x + 4 = 18
18 = 9x
4.) 5(x + 3) = 5x + 15
Prop: ____________
Prop: ____________
November 22, 2016
State the property that justifies each statement.
5.) If x = 7, and
y = x,
then y = 7
prop: _______
6.) If AB = x + 5, and
AB = 15, then
x + 5 = 15
7.) AB = AB
8.) If 5x = 30
prop: _______
prop: _______
prop: _______
then 5x = 30
5
5
Homework
p.137 # 1-4, 9-17, 20