For any numbers \(a\), \(b\), and \(c\),
if
$$a = b$$
then
$$a + c = b + c$$
In words: When the same value is added to both sides of a true equation, the meaning of the new equation remains true and the same.
Example 1:
$$\eqalign{
4 &= 4 \cr
4 \color{red}{+ 3} &= 4 \color{red}{+ 3} \cr
7 &= 7 \cr} $$
Example 2:
$$\eqalign{
- 1 &= - 1 \cr
- 1 \color{red}{+ \left( { - 2} \right)} &= - 1 + \color{red}{\left( { - 2} \right)} \cr
- 3 &= - 3 \cr} $$
Example 3:
$$\eqalign{
x &= 8 \cr
x \color{red}{+ 5} &= 8 \color{red}{+ 5} \cr
x + 5 &= 13 \cr} $$