To solve the given equation step by step, let's start by simplifying the expression inside the brackets and the braces.
Given equation:
[tex]\[ x - \{2 + [x - (3x - 1)]\} = 2 - x \][/tex]
First, simplify the innermost expression [tex]\( 3x - 1 \)[/tex]:
[tex]\[ x - (3x - 1) = x - 3x + 1 = -2x + 1 \][/tex]
Now substitute this back into the equation:
[tex]\[ x - \{2 + [ -2x + 1 ]\} = 2 - x \][/tex]
Next, simplify inside the brackets:
[tex]\[ 2 + [ -2x + 1 ] = 2 - 2x + 1 = 3 - 2x \][/tex]
Now substitute this back into the equation:
[tex]\[ x - \{3 - 2x\} = 2 - x \][/tex]
Simplify inside the braces:
[tex]\[ x - (3 - 2x) = x - 3 + 2x = 3x - 3 \][/tex]
So now our equation is:
[tex]\[ 3x - 3 = 2 - x \][/tex]
Combine like terms by adding [tex]\( x \)[/tex] to both sides:
[tex]\[ 3x + x - 3 = 2 \][/tex]
[tex]\[ 4x - 3 = 2 \][/tex]
Add 3 to both sides to isolate the term with x:
[tex]\[ 4x = 5 \][/tex]
Finally, divide both sides by 4 to solve for [tex]\( x \)[/tex]:
[tex]\[ x = \frac{5}{4} \][/tex]
Thus, the value of [tex]\( x \)[/tex] is [tex]\(\boxed{\frac{5}{4}}\)[/tex].
