# Inequalities and regions

**Vertical regions**

Graphs can be used to represent inequalities by **regions **(region is the area where all points obey a given rule).

For example, the region for *x* > 2 is represented by:

In the graph, the area where the graph is *x* > 2 is shown above. In this area, all of the points would be more than 2.

The line which intersects where *x* = 2 is drawn with a dotted line.

In the right region of the line *x* = 2, every point represents *x* > 2.

In the left region of the line *x* = 2, every point represents *x* < 2.

**Horizontal regions**

The rules for horizontal regions will follow the rules for the vertical regions. Therefore the graph which represents *y* ≤ 3 is:

In the graph, the area where the graph is *y* ≤ 3 is shown above. In this area, all of the points would be more than or equal to 3.

The line which intersects where *y* = 3 is drawn with a solid line.

In the top region of the line *y* = 3, every point represents *y* > 3 and *y* = 3

In the left region of the line *y* = 3, every point represents *y* < 3 and *y* = 3

**Horizontal and vertical regions combined**

When combining horizontal and vertical regions, the *unwanted* regions are shaded out. This enables the required area to be easily identified.

In the graph above, the regions represent –4 < *x* < –1 and –1 < *y *≤ 3.

The regions which are unshaded represent –4 < *x* < –1 and –1 < *y *≤ 3.