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