Solve linear equations using the addition and multiplication
properties of equality. Two important properties that are used
in producing equivalent equations are the addition property of equality
and the multiplication property of equality.
Addition and Multiplication Properties of Equality
Addition Property of Equality
For all real numbers A, B, and C, the equations
A = B and A + C = B + C
are equivalent.
In words, the same number may be added to each side of an equation
without changing the solution set.
Multiplication Property of Equality
For all real numbers A and B, and for C ≠ 0, the equations
A = B and AC = BC
are equivalent.
In words, each side of an equation may be multiplied by the same
nonzero number without changing the solution set.