Solve -2x-2/x+5<0

$$\frac { - 2 x - 2 } { x + 5 } < 0$$

Solve for x

$$x\in \left(-\infty,-5\right)\cup \left(-1,\infty\right)$$

Solution Steps

For the quotient to be negative, -2x-2 and x+5 have to be of the opposite signs. Consider the case when -2x-2 is positive and x+5 is negative.

$$-2x-2>0 x+5<0$$

The solution satisfying both inequalities is x<-5.

$$x<-5$$

Consider the case when x+5 is positive and -2x-2 is negative.

$$x+5>0 -2x-2<0$$

The solution satisfying both inequalities is x>-1.

$$x>-1$$

The final solution is the union of the obtained solutions.

$$x<-5\text{; }x>-1$$