Chapter 3 - Solving Inequalities - 3-2 Solving Inequalities Using Addition or Subtraction - Practice and Problem-Solving Exercises - Page 175: 39

$n\lt -\frac{8}{3}$

$\frac{1}{3}\lt n+3$ $\mathrm{Switch\:sides}:$ $n+3>\frac{1}{3}$ $\mathrm{Subtract\:}3\mathrm{\:from\:both\:sides}:$ $n+3-3>\frac{1}{3}-3$ $\mathrm{Simplify}$ $n\gt\frac{1}{3}-3$ $n\gt\frac{1}{3}-3(\frac{3}{3})$ $n\gt\frac{1}{3}-\frac{9}{3}$ $n>-\frac{8}{3}$ $\mathrm{check}:$ $n=-1$ $-\frac{8}{3}\lt-1$ $\mathrm{true}$