## Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

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.