I don't understand the second step in the solution procedure. Please explain.

Muhammad, suppose 1-x is k and (1-x)*=k*
k*=1-k acc to the definition of the operator *
Substitute 1-x back for k, and you have 1-(1-x).

x*=muham + x
(mad)*=1
muham + mad = 1

That was just for fun.
I don't know whether Arcadia already helped you, if so, consider me just rambling on stuff you already know ;)
Technically you refer to the third line of the solution ergo (1-1+x)*=(1-x)* which is the second step in the solution.
Only the left side has changed here, from ( 1 - ( 1 - x ))* to ( 1 - 1 + x )*
If it would have been ( 1 + ( 1 - x ))* it would have solved into ( 1 + 1 - x )*
The difference is the leading minus sign, so we'll have to multiply each factor with negative 1 before being able to get rid of the parentheses.
-(whatever) ergo -1(whatever) becomes +(-whatever) get rid of parentheses make -whatever

You could also apply your newly acquired function/algorithm ergo the defined operator at once:

Given:
x* = 1 - x

We start with:
((1 − x)*)* = (1 − x)*

Solve all operators and we'll get:
1 - ( 1 - ( 1 - x )) = 1 - ( 1 - x )

Start to solve the leading minus signs from inner to outer parentheses to get rid of them all:
1 - ( 1 + ( -1 + x )) = 1 + ( -1 + x )
1 - ( 1 -1 + x ) = 1 -1 + x
1 +( -1 +1 - x ) = 0 + x
1 -1 +1 - x = x
1 - x = x
Subtract x on both sides:
1 - 2x = 0
Subtract 1 on both sides:
- 2x = - 1
Divide both sides by negative 2:
x = -1 / -2 ergo 1/2
x = 1/2 and that's our answer


Niels

Greetings from Holland

i dont understand D: can someone explain

The symbol is like a function. When given an equation/function, x*=1-x, whatever's within * will equal the left part of the first equation/function.
x*=1-x
(1-x)*=1-(1-x)
(1-x) on the second equation acts like x from the first equation.

How come nobody posts on here anymore?

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