Solve for x
x\in \left(-1,0\right)
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-4x^{2}-4x>0
Use the distributive property to multiply -4x by x+1.
4x^{2}+4x<0
Multiply the inequality by -1 to make the coefficient of the highest power in -4x^{2}-4x positive. Since -1 is negative, the inequality direction is changed.
4x\left(x+1\right)<0
Factor out x.
x+1>0 x<0
For the product to be negative, x+1 and x have to be of the opposite signs. Consider the case when x+1 is positive and x is negative.
x\in \left(-1,0\right)
The solution satisfying both inequalities is x\in \left(-1,0\right).
x>0 x+1<0
Consider the case when x is positive and x+1 is negative.
x\in \emptyset
This is false for any x.
x\in \left(-1,0\right)
The final solution is the union of the obtained solutions.
Examples
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Simultaneous equation
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\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
Integration
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Limits
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