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To solve a quadratic inequality such as x2-6x+8>0 the best approach is to find the critical values of x which make the value of the function 0 and sketch the graph. Here we can factorise so we see that we require (x-2)(x-4)>0 We are looking for values of x to make x2-6x+8 positive. We see that y is positive when x>4 and when x<2.

Note the link to another Desmos page where you can look at further quadratic functions.

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If you wish to see some worked examples and try some exercises you could check The Maths Teacher – See Algebra AS Level – Inequalities: Linear and Quadratic. Note the choice of video / transcript or go straight to the exercise with worked solutionsYou may find other useful resources here too.

You could of course use WolframAlpha to check the solution to any inequalities and generate as many examples as you want. Simply type in the inequality and plot as well as the he solutions will be returned.

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