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:

$$\eqalign{
   4 &= 4  \cr 
   4\left( {\color{red}{ – 3}} \right) &= 4\left( {\color{red}{ – 3}} \right)  \cr 
    – 12 &=  – 12 \cr} $$