Properties of Equality

For all real numbers $x$ , $x=x$ .

A number equals itself.

For all real numbers $x\text{and}y$ ,

if $x=y$ , then $y=x$ .

Order of equality does not matter.

For all real numbers $x,y,\text{and}z$ ,

if $x=y$ and $y=z$ , then $x=z$ .

Two numbers equal to the same number are equal to each other.

For all real numbers $x,y,\text{and}z$ ,

if $x=y$ , then $x+z=y+z$ .

For all real numbers $x,y,\text{and}z$ ,

if $x=y$ , then $x-z=y-z$ .

For all real numbers $x,y,\text{and}z$ ,

if $x=y$ , then $xz=yz$ .

For all real numbers $x,y,\text{and}z$ ,

if $x=y$ , and $z\ne 0$ ,

then $\frac{x}{z}=\frac{y}{z}$ .

For all real numbers $x\text{and}y$ ,

if $x=y$ , then $y$ can be substituted for $x$ in any expression.

For all real numbers $x,y,\text{and}z$ ,

$x\left(y+z\right)=xy+xz$