#### Answer

identity

#### Work Step by Step

Using the properties of equality, the solution to the given equation, $
3(x-4)+2=x+2(x-5)
$, is
\begin{array}{l}\require{cancel}
3(x)+3(-4)+2=x+2(x)+2(-5)
\\\\
3x-12+2=x+2x-10
\\\\
3x-x-2x=-10+12-2
\\\\
0=0
\text{ (TRUE)}
.\end{array}
Since the solution above ended with a TRUE statement, then the given equation is an identity.