Algebraic proofs  Logic
Algebraic proofs
Lessons
Notes:
Let
$a,b,$
and
$c$
be real numbers. Then here are some of the properties of equality:
Reflexive Property: For every number $a$, then $a=a$.
Symmetric Property: For all numbers
$a$
and
$b$
, if
$a=b$
, then
$b=a$
.
Transitive Property: If
$a=b$
and
$b=c$
, then
$a=c$
.
Substitution Property: If
$a=b$
, then
$b$
can be substituted for
$a$
in any equation.
Addition Property: If
$a=b$
, then
$a+c=b+c$
.
Subtraction Property: If
$a=b$
, then
$a?c=b?c$
.
Multiplication Property: If
$a=b$
, then
$a\cdot c=b\cdot c$
.
Division Property: If
$a=b$
, then
$\frac{a}{c}=\frac{b}{c}$
.
Distribution Property:
$a(b+c)=ab+ac$
When you solve an equation, you will want to use to the twocolumn proof. For example, if you want to show that
$x=1$
for the equation
$2(x+1)+1=5$
, then it will look like this:
Statements  Reasons 
$2(x+1)+1=5$  Given 
$2x + 2 + 1 =5$  Distributive Property 
$2x=2$  Subtraction Property 
$x=1$  Division Property 

Intro Lesson
Algebraic Proofs Overview:

1.
Understanding the Properties of Equality
State which property was used in each statement: