Subtraction Property of Equality

For any numbers \(a\), \(b\), and \(c\),

if 

$$a = b$$

then

$$a – c = b – c$$

In words: When you subtract the same value to both sides of a true equation, the new equation remains true and retains the same meaning. 

Example 1:

$$\eqalign{
   9 &= 9  \cr 
   9\color{red}{ – 5} &= 9 \color{red}{- 5}  \cr 
   4 &= 4 \cr} $$

Example 2:

$$\eqalign{
    – 2 &=  – 2  \cr 
    – 2 \color{red}{- \left( { – 7} \right)} &=  – 2 \color{red}{- \left( { – 7} \right)} \cr 
   5 &= 5 \cr} $$

Example 3:

$$\eqalign{
   y &= 7  \cr 
   y \color{red}{- 5} &= 7 \color{red}{- 5}  \cr 
   y – 5 &= 2 \cr} $$