Solve for a
a\in \left(0,2\right)
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-2a+a^{2}<0
Multiply the inequality by -1 to make the coefficient of the highest power in 2a-a^{2} positive. Since -1 is negative, the inequality direction is changed.
a\left(a-2\right)<0
Factor out a.
a>0 a-2<0
For the product to be negative, a and a-2 have to be of the opposite signs. Consider the case when a is positive and a-2 is negative.
a\in \left(0,2\right)
The solution satisfying both inequalities is a\in \left(0,2\right).
a-2>0 a<0
Consider the case when a-2 is positive and a is negative.
a\in \emptyset
This is false for any a.
a\in \left(0,2\right)
The final solution is the union of the obtained solutions.
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Limits
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