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Inequalities - OCRGraphs of inequalities - Higher

Inequalities show the relationship between two expressions that are not equal to one another. Inequalities are useful when projecting profits and breakeven figures. In this OCR Maths study guide, you can revise the more than and less than signs, how to solve inequalities and how inequality can be represented graphically.

Part of MathsAlgebra

Graphs of inequalities - Higher

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

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

Graph showing the inequality x < -1 and the region where the x coordinates are less than -1 is shaded

Example

Show the region satisfied by the inequality \(-2 \textless x \leq 3\).

Identify the two regions shown by the inequalities. These are \(2 \textless x\) (or \(x \textgreater -2\)) and \(x \leq 3\).

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

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

\(x\) is the values in between these two inequalities, so shade this region.

Graph showing the inequalities of x = -2 and x = 3

Question

Show the region satisfied by the inequalities \(-4 \leq y \textless 0\) and \(y \geq x\).