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__Linear Inequalities__

Consider this linear inequality:

To solve for x, we need to do what we do when we solve equations. We see that:

However, when we divide both sides of an inequality by a negative number, we also have to reverse the inequality sign, like below.

The graph for this inequality is x = -1, but every value less than -1 is shaded. As the inequality sign is 'less than', the line is dotted. However, if you have an inequality sign of greater than or equal to or less than or equal to, the line will not be dotted.

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__Quadratic Inequalities__

Consider this quadratic inequality:

To solve for x, we need to first factorise the left hand side of the inequality.

Now we must sketch the graph to see where the values of y are greater than 0.

Here we see that y is greater than 0 where x is more than -1 and less than -2, so the answer to this inequality will be:

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