# Chapter 2 - Equations, Inequalities, and Problem Solving - Review Exercises: Chapter 2 - Page 149: 25

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.

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