Solve for x
x\in \left(-\infty,-\frac{4}{3}\right)\cup \left(-1,\infty\right)
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3x+4<0 x+1<0
For the product to be positive, 3x+4 and x+1 have to be both negative or both positive. Consider the case when 3x+4 and x+1 are both negative.
x<-\frac{4}{3}
The solution satisfying both inequalities is x<-\frac{4}{3}.
x+1>0 3x+4>0
Consider the case when 3x+4 and x+1 are both positive.
x>-1
The solution satisfying both inequalities is x>-1.
x<-\frac{4}{3}\text{; }x>-1
The final solution is the union of the obtained solutions.
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