Chapter 2 - Equations, Inequalities, and Problem Solving - 2.2 Using the Principles Together - 2.2 Exercise Set - Page 94: 27

$n=-2.8$

Using the properties of equality, the solution to the given equation, $ 5.3+1.2n=1.94 $, is \begin{array}{l} 1.2n=1.94-5.3 \\\\ 1.2n=-3.36 \\\\ n=\dfrac{-3.36}{1.2} \\\\ n=-2.8 .\end{array} Checking: \begin{array}{l} 5.3+1.2(-2.8)=1.94 \\\\ 5.3-3.36=1.94 \\\\ 1.94=1.94 \text{ (TRUE)} .\end{array} Hence, the solution is $ n=-2.8 .$