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Addition Property of Equality

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:

$$\eqalign{
   x &= 8  \cr 
   x \color{red}{+ 5} &= 8 \color{red}{+ 5}  \cr 
   x + 5 &= 13 \cr} $$

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