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Whenever you multiply (or divide) both sides an inequality by a negative number.

Example: 3 < 5, therefore -3 > -5

-2x < 10

becomes (by multiplying by -1/2):

x > 5

x(x+1) > 0

In this type of inequality, you can divide both sides by x, but you have to consider the two cases, that x > 0 and that x < 0.

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