Before we get stuck in to this topic, it’s important to understand what an inequality is and how it works. If you’re not sure, click here (https://mathsmadeeasy.co.uk/gcse-maths-revision/inequalities-number-line-solving-inequalities/) for more info. Additionally, you will need to know how to draw straight-line graphs, more on that here (https://mathsmadeeasy.co.uk/gcse-maths-revision/drawing-straight-line-graphs-gcse-maths-revision-worksheets/).
In this topic, we are going to be looking at how to express multiple inequalities on a graph, and then how to read a graph to determine what inequalities it is expressing.
The way to express an inequality on a number line is as follows:
– Firstly, make the subject. Then, treat the inequality as if it were an equation and plot the straight line. You should plot a solid line if the inequality is inclusive (i.e. ) and a dashed line if it is a strict inequality (i.e. ).
– Identify which side of the line the area that satisfies the inequality is on:
– If it is a greater than (or equal to) – – then you want the area above the line,
– If it is a less than (or equal to) – – then you want the area below the line.
– Shade the area that you identified in step 2.
A caveat to this is if you can’t make the subject, e.g. with an inequality such as . We still plot the line as if it were an equation, but you can’t shade “above” or “below” a vertical line like . Instead, the area you want is to the right of it, where the values are bigger than 3. By extension, if you were given then you would shade to the left of the line.
Example: Shade the area that satisfies the inequality and mark it an A.