Solve 5-2x/2+x<0

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

Solve for x

$$x\in \left(-\infty,-2\right)\cup \left(\frac{5}{2},\infty\right)$$

Solution Steps

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

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

The solution satisfying both inequalities is x<-2.

$$x<-2$$

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

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

The solution satisfying both inequalities is x>\frac{5}{2}.

$$x>\frac{5}{2}$$

The final solution is the union of the obtained solutions.

$$x<-2\text{; }x>\frac{5}{2}$$