For any numbers \(a\), \(b\), and \(c\),
if
$$a = b$$
then
$$a - c = b - c$$
In words: When the same value is subtracted from both sides of a true equation, the meaning of the new equation remains true and the same.
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:
$$\eqalign{
y &= 7 \cr
y \color{red}{- 5} &= 7 \color{red}{- 5} \cr
y - 5 &= 2 \cr} $$