Solve for x
x\in \left(-3,5\right)
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x+3>0 x-5<0
For the product to be negative, x+3 and x-5 have to be of the opposite signs. Consider the case when x+3 is positive and x-5 is negative.
x\in \left(-3,5\right)
The solution satisfying both inequalities is x\in \left(-3,5\right).
x-5>0 x+3<0
Consider the case when x-5 is positive and x+3 is negative.
x\in \emptyset
This is false for any x.
x\in \left(-3,5\right)
The final solution is the union of the obtained solutions.
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