#### Answer

a. Yes, x=2 is a solution of the given equation.
b. No, x=4 is not a solution of the given equation.

#### Work Step by Step

Simplify the given equation:
1. $1-[2-(3-x)]=4x-(6+x)$
2. Distribute the negative sign inside of the brackets:$1-(2-3+x) = 4x-(6+x)$
3. Distribute the negative signs on the left and right side of the equation: $1-2+3-x=4x-6-x$
4. Simplify both sides of the equation: $2-x=3x-6$5. Add 6 to both sides of the equation:$8-x=3x$
5. Add x to both sides of the equation: $8=4x$
a. Plug in x=2 to see if it makes the equation true: $8=4(2)$
$8=8$ the equation is true so yes, x=2 is a solution of the given equation.
b. Plug in $x=4$ to see if it makes the equation true: $8=4(4)$ $8=16$ the equation is not true so x=4 is not a solution of the given equation.