Graphical Inequalities – GCSE Maths Revision and Worksheets

What you need to know:

You may be asked to either: present several inequalities on a graph and shade the area that satisfies them all, or given a graph with a certain section shaded, write down the inequalities that would produce that graph. The inequalities may be straightforward, a restriction on x or a restriction on y, but they can also introduce more difficult inequalities by including two variables.

Fortunately, this follows the same pattern as with previous inequalities: treat it like an equation in the beginning. Suppose the inequality in question was 2y - 4x > 1. Then we see 2y - 4x = 1 can be rearranged to y = 2x + \frac{1}{2} which is clearly a graph of a straight line with gradient 2, and y-intercept \frac{1}{2}. You can then plot this straight line graph, and furthermore determine which side of the line satisfies your inequality (this can be done by testing individual coordinates if you aren’t sure). The only other thing you must be careful with is that if you have a strict inequality (<, >) then your straight lines should be dashed, but if it is inclusive (\leq, \geq) then the straight line should be a normal, solid line.