Sure, let's solve this equation step-by-step.
We start with the given equation:
[tex]\[ 2(x-1) + 3(x-2) - 5(x+3) = 8 \][/tex]
First, distribute each term:
[tex]\[ 2(x - 1) + 3(x - 2) - 5(x + 3) = 8 \][/tex]
[tex]\[ 2x - 2 + 3x - 6 - 5x - 15 = 8 \][/tex]
Next, combine like terms:
[tex]\[ (2x + 3x - 5x) + (-2 - 6 - 15) = 8 \][/tex]
[tex]\[ 0x - 23 = 8 \][/tex]
[tex]\[ -23 = 8 \][/tex]
This is a contradiction because [tex]\(-23\)[/tex] does not equal [tex]\(8\)[/tex]. Therefore, the original equation has no solution.
Since no values of [tex]\( x \)[/tex] satisfy the equation, there are no solutions, and thus the solution set is empty.
[tex]\[ \boxed{\emptyset} \][/tex]
