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Subtraction 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 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:

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

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Properties of Equality
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