Graphically this can be done in two dimensions by drawing lines or curves so that they enclose the desired region. A single inequality is represented by shading the space to the left or to the right of the line or the inside or outside of a curve (which could be a circle, ellipse, parabola, hyperbola, etc.). For example, y≥x+3 would refer to the space above the line y=x+3, while y≤x+3 would refer to the space below the line.
x2+y2≤1 would refer to the finite area of a circle radius 1, while x2+y2≥1 would be the whole of space less the circle, that is, the whole region outside the circle, but including its circumference.
y≥x2 or x≥y2 would be space inside the parabola. So by graphing several inequalities you can enclose an area or region common to all the inequalities. If you use shading to show the relevant areas referred to by each inequality, the desired region will be where all the shadings overlap.
The most common way of using inequalities to define a region is to use three straight lines which intersect to form a triangle. Each intersection is a vertex. You can then look at each line and see whether the region is to the left or right of the line so that you know whether to use ≥ or ≤ respectively.
4 lines would be used to define a quadrilateral region, and you could use, for example, two lines and a circle to form all sorts of regions with curved and straight borders.
For best results use graphs so that you can clearly visualise the desired region and determine the nature of the inequalities.