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You see it all the time in algebra.

4x + 8 = 10

Now subtract 8 from both sides:

4x + 8 - 8 = 10 - 8

4x = 2

The rule you are using in this step is the "subtraction property of equality"

I don't think you need more examples to understand it. Just if you ever find yourself subtracting the same amount from both sides... you've just invoked the property.

:)