Algebraic proofs

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 two-column 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