1. Algebraic proofs
A proof is an argument that uses logic to show that a conclusion is true.
Every time you solved an equation in Algebra you were performing a proof since an algebraic proof uses properties of equality to solve an equation.

2. Properties of Equality
Addition prop of Equality
Subtraction prop of equality
Multiplication prop of equality
Division prop of equality
Symmetric prop of equality
Reflexive prop of equality
Transitive prop of equality
Substitution prop of equality
Example
If a=b, then a+ c = b +c
If a=b, then a-c= b-c
If a = b, then ac = bc
If a= b, c=0, then a/c=b/c
If a= b, then b=a
a=a
If a= b and b= c, then a =c
If a= b, then b can be substituted for a in any expression

3. Algebraic Proof
An algebraic proof shows step by step how a problem is solved.
Whenever a step requires that you perform basic mathematical operations on a single side of an equation( like add, subtract, multiply or divide), the step is justified by the term, “simplify”

4. Most proofs begin by presenting the facts of a problem.
The first line restates what you have been told, and is justified as "Given"

5. Writing an algebraic proof Solve this equation. Justify each step
Writing an algebraic proof Solve this equation . Justify each step (x+1) = x+9
2(x+1)= x+9
2x+2= x+9
2x+2-2= x+9-2
2x= x+7
2x-x= x+7-x
X=7
Given
Distributive property
Subtr prop of equality
Simplify
simplify

6. 3x-1 = 2x
3x-1 = 2x+3
15(3x-1)=15(2x+3)
9x-3 = 10x +15
9x -3 +3= 10x
9x = 10x + 18
9x -10x =10x x
-x = 18
-x(-1) = 18(-1)
X = -18
Given
Mult prop of equality
Associative prop of mult
Distributive prop
Add prop of equality
Simplify
Subtr prop of equality
simplify

7. Give justification for each step.
a = -4 1) 2) 3) 4) 5) 6)