Adding the same number to both sides of a given equation yields an equivalent equation. Let a, b, and c be real numbers.
Given an equation, subtracting the same number from each side of the equation yields an equivalent equation. Let a, b, and c be real numbers.
Given an equation, multiplying each side of the equation by the same number yields an equivalent equation. Let a, b, and c be real numbers.
If a=b, then a×c=b×c.
Dividing each side of an equation by the same nonzero number yields an equivalent equation. Let a, b, and c be real numbers.
If a=b and c≠0, then a÷c=b÷c.
For any real number, the number is equal to itself.
a=a
For all real numbers, the order of an equality does not matter. Let a and b be real numbers.
If a=b, then b=a.
For all real numbers, if two numbers are equal to the same number, then they are equal to each other. Let a, b, and c be real numbers.
If a=b and b=c, then a=c.
If two real numbers are equal, then one can be substituted for another in any expression.
If a=b, then a can be substituted for b in any expression.