This paper describes two new functions implemented in Mathematica, IneqPlot and ComplexIneqPlot, for plotting inequalities in two real variables. The first function creates a plot showing the region in the plane whose points satisfy a given inequality. The second function creates a plot showing the region in the complex plane whose points satisfy a given inequality. In contrast to the standard Mathematica functions: RegionPlot and ComplexRegionPlot, these new functions place special emphasis on drawing boundaries according to the type of inequality and on plotting inequalities involving piecewise functions (floor function, ceiling function, etc.). To illustrate how Mathematica is a powerful tool for this task, detailed and practical examples are provided using the standard Mathematica functions and the new functions implemented by the authors. These new functions are coded based on the standard function RegionPlot but include an additional analysis to draw the borders according to the type of inequality proposed. After viewing and comparing the results, we can say that we provide users with an excellent computational tool for teaching and visualization.