The boundary lines $\displaystyle{y}=-{1}\usepackage{cmbright}\Huge\$ , $\displaystyle{y}={2}\usepackage{cmbright}\Huge\$ are shown as solid lines, thus the $\displaystyle\le\usepackage{cmbright}\Huge\$ symbol. The boundary line $\displaystyle{y}={3}{x}-{4}\usepackage{cmbright}\Huge\$ is shown as a dashed line, thus the $\displaystyle<\usepackage{cmbright}\Huge\$ symbol. Test a point inside the region to see if it makes these inequalities true. For example, the point $\displaystyle{\left({4},{1}\right)}\usepackage{cmbright}\Huge\$ is inside the region. Substituting in the first inequality gives you $\displaystyle-{1}\le{1}\le{2}\usepackage{cmbright}\Huge\$ , which is true. Substituting in the second inequality gives you $\displaystyle{1}<{12}-{4}\usepackage{cmbright}\Huge\$ , or $\displaystyle{1}<{8}\usepackage{cmbright}\Huge\$ , which is true.