Multiplication Property of Equality
For any numbers \(a\), \(b\), and \(c\),
if
$$a = b$$
then
$$ac = bc$$
In words: When you multiply the same value to both sides of a true equation, the new equation remains true and retains the same meaning.
Example 1:
$$\eqalign{
3 &= 3 \cr
3\left( \color{red}{6} \right) &= 3\left( \color{red}{6} \right) \cr
18 &= 18 \cr} $$
Example 2:
$$\eqalign{
4 &= 4 \cr
4\left( {\color{red}{ – 3}} \right) &= 4\left( {\color{red}{ – 3}} \right) \cr
– 12 &= – 12 \cr} $$