Question 393286
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The first thing to explain is that the equals sign is like a balance scale.  You can change the value any way you want on one side of the equals sign as long as you make the same value change on the other side to match it.


The trick is to manipulate things so that you have your blank line on one side and a single number on the other side so that the mathematical sentence reads, [blank] is equal to [some number] (or [some number] is equal to [blank] -- either way, it doesn't matter).


On the left side (I abbreviate LHS), you can do the indicated arithmetic.  That doesn't change the value in the LHS, so you don't have to do anything to balance it in the RHS.  60 minus 20 = 40, so rewrite your equation:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 40\ =\ 20\ +\ \underline{\text{     }}]


So now you can see that the RHS has a 20 in it that we would like to eliminate, so add -20 to both sides (has to be both sides because if you reduce the value of the RHS by 20, you have to reduce the value of the LHS to keep the equation in balance):


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 40\ +\ (-20)\ =\ 20\ +\ (-20)\ +\ \underline{\text{     }}]


Now just do the arithmetic.  40 plus a minus 20 is 20, and 20 plus a minus 20 is 0 leaving only the blank line in the RHS.


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 20\ =\ \underline{\text{     }}]


And that's your answer.


John
*[tex \LARGE e^{i\pi} + 1 = 0]
My calculator said it, I believe it, that settles it
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