What same number may be added to or subtracted from both sides of an equation with out changing the solution fo the equation?

Answer 1

Any number at all has the specified property.

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As correctly noted above, if you are performing exactlythe same operation (in this case adding or subtracting the same specific number) to both sides of an equation then it does not matter what number you use. Any number whatsoever may be used. This is because both sides will remain balanced.

Here is a concrete example:

Suppose 2x = 14

We could solve this as:

2x = 14

x = 14/2

x = 7

But we could also write the above equation as:

2x + 3 = 14 + 3

for:

2x + 3 = 14 + 3

2x + 3 = 17

2x = 17 -3

2x = 14 (we have reached the same position as above!)

x = 14/2

x = 7

You could substitute any number whatsoever and we will always end up with x = 7 here.