The boundary line $\displaystyle{y}={1}\usepackage{cmbright}\Huge\$ is shown as a dashed line meaning it is not included in the solution, thus the $\displaystyle<\usepackage{cmbright}\Huge\$ symbol in $\displaystyle{1}<{y}\usepackage{cmbright}\Huge\$ . The boundary lines $\displaystyle{y}={3}\usepackage{cmbright}\Huge\$ and $\displaystyle{y}=-{2}{x}+{2}\usepackage{cmbright}\Huge\$ are shown as solid meaning they are included in the solution, thus the $\displaystyle\le\usepackage{cmbright}\Huge\$ and $\displaystyle\ge\usepackage{cmbright}\Huge\$ symbol in those inequalities. Test a point inside the region to see if it makes these inequalities true. For example, the point $\displaystyle{\left({3},{2}\right)}\usepackage{cmbright}\Huge\$ is inside the region. Substituting in the first inequality gives you $\displaystyle{1}<{2}\le{3}\usepackage{cmbright}\Huge\$ , which is true. Substituting in the second inequality gives you $\displaystyle{2}\ge-{6}+{2}\usepackage{cmbright}\Huge\$ , or $\displaystyle{2}\ge-{4}\usepackage{cmbright}\Huge\$ , which is true.