# Graphs of inequalities - Higher

An inequality can be represented graphically as a region on one side of a line.

Inequalities that use < or > symbols are plotted with a dashed line to show that the line is not included in the region. Inequalities that use ≤ or ≥ symbols are plotted with a solid line to show that the line is included in the region.

For example, this graph shows the inequality . This can be seen as there is a dashed line at , and the region where the coordinates are less than -1 is shaded.

### Example

Show the region satisfied by the inequality .

Identify the two regions shown by the inequalities. These are (or ) and .

: draw a dotted line at . is the graph made by coordinates points where is equal to -2, for example (-2, 5), (-2, 4), (-2, 3), (-2, 2) and so on.

: draw a solid line at . is the graph made by coordinate points where is equal to 3, for example (3, -4), (3, -3), (3,-2), (3, -1) and so on.

is the values in between these two inequalities, so shade this region.

Question

Show the region satisfied by the inequalities and .

Identify the regions shown by the inequalities. These are , and .

: draw a solid line at . This line is made by the coordinate points where , for example (5, -4) or (-5, -4). is greater than or equal to -4, so shade the points above the line.

: draw a dashed line at . This line goes through all the coordinate points where (it is the same as the -axis). is less than 0, so shade all the points below this line.

: draw a solid line at . To draw the line , plot coordinate points where the coordinate is equal to the coordinate, for example (4, 4), (2, 2), (-1, -1) and so on. is greater than or equal to , so shade the region above this line.

The answer is the region where the three shaded regions all overlap.

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