Download Reasoning with Properties from Algebra

Reasoning with Properties from
Algebra
Properties of Equality
Addition
If a = b, then:
(Subtraction) a + c = b + c
Property of
a–c=b–c
Equality
If x + 8 = 20,
Then x = 12
Why?
Subtract Prop. of =
Properties of Equality
Multiplication
(Division)
Property of
Equality
If a = b, then:
ac = bc
a b

c c
If 4x = 32,
Then x = 8
Why?
Division Prop. of =
Properties of Equality
Reflexive Prop.
of =
Symmetric
Prop. of =
a=a
3=3
Why? Reflex Prop =
If a = b,
then b = a.
If 54 = x, then x=54
Why? Symm. Prop =
Properties of Equality
Transitive If a = b and
If 2x = y and y = 48,
Prop. of = b = c, then a = c
then 2x = 48
Why? Transitive Prop.
Substitution If a = b, then a If 4x + 5 = 3y and
Prop. of =
can replace b
x =-2, then
in an equation
4(-2) + 5 = 3y
Why? Substitution Prop.
Distributive Property
a(b + c) = ab + ac. -x(3x + 2) = 27
a(b – c) = ab – ac. -3x2 – 2x = 27
Why? Distributive Prop.
Solve: 5x – 18 = 3x + 2
and give a reason for each step.
Step
5x – 18 = 3x + 2
2x – 18 =
2
2x
=
20
x
=
10
Reason
Given
Subtraction POE
Addition POE
Division POE
Solve: 55z – 3(9z + 12) = -64
and give a reason for each step.
Step
55z – 3(9z + 12) = -64
55z – 27z – 36 = -64
28z – 36 = -64
28z
= -28
z
= -1
Reason
Not Multiplication
Property!!!
Given
Distributive Prop
Simplify
Addition POE
Division POE
What is the reason for each step
in the solution?
Step
Reason
1.
1. Given
2. 10 – 8n = –6
3.
– 8n = –16
2. Multiplication POE
3. Subtraction POE
4.
4. Division POE
n=2