Answer
the set of all real numbers
Work Step by Step
Using the properties of equality, the given equation, $
8x-(1-x)=3(1+3x)-4
,$ is equivalent to
\begin{array}{l}\require{cancel}
8x-1+x=3+9x-4
\\\\
8x+x-9x=3-4+1
\\\\
0=0 \text{ (TRUE)}
.\end{array}
Since the solution above ended with a TRUE statement, then the given equation is an identity. Hence, the solution is $\text{
the set of all real numbers
}.$