Chapter 1 - 1.7 - Linear Inequalities in One Variable - 1.7 Exercises - Page 137: 42

$2\lt x\lt 6$ See graph

For $$1.6\lt0.3x+1$$ $$1.6-1\lt0.3x+1-1$$ $$0.6\lt0.3x$$ $$\frac{0.6}{0.3}\lt\frac{0.3x}{0.3}$$ $$2\lt x$$ $$x\gt 2$$ For $$0.3x+1\lt 2.8$$ $$0.3x+1-1\lt2.8-1$$ $$0.3x\lt 1.8$$ $$\frac{0.3x}{0.3}\lt\frac{1.8}{0.3}$$ $$x\lt 6$$ Combining: $$x\gt2\text{ and }x\lt 6$$ $$2\lt x\lt 6$$ The graph of the solution set is as shown.