Question

______ number can be added to both sides of equation.

Answer 1

Answer:

any no. can be added to both sides of the equation

Answer 2

Here's one way of looking at it: if a=b, then f(a)=f(b), no matter the function f(x).

From this point of view, solving an equation amounts to applying a sequence of functions in order to generate an equation whose solutions are easy to read off. What this sort of argument shows is that the new equations are logical consequences of the original equation.

So, for example, suppose you're given that

x+1=2

and you want to subtract one from both sides. Then just apply the function f(s)=s−1, yielding

x=f(x+1)=f(2)=1