Why must you always do the same thing to both sides of an equation

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Why must you always do the same thing to both sides of an equation

Mathematics
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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if it's an equation then left side equals right side. think of it like this: say you have a balance with two coins and you add 5 coins to one side.. it nolonger becomes equal so you add 5 coins to the other side to equal it out. doing the same thing to both sides
3=3 does 5+3=5+3 still hold?
how about 3-4=3-4?

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Other answers:

3/5=3/5? 3*6=3*6?
how about ln(3)=ln(3) and 3^2=3^2 and 3^3=3^3
i notice how i have done the same thing to both sides otherwise the lhs wouldn't be equal to the rhs like if i done something to lhs of 3=3 and got 3^3=3 well that just isn't true since 27 does not equal 3

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