Solve 2(m+1)/m-2<0

$$\frac { 2 ( m + 1 ) } { m - 2 } < 0$$

Solve for m

$$m\in \left(-1,2\right)$$

Solution Steps

Use the distributive property to multiply 2 by m+1.

$$\frac{2m+2}{m-2}<0$$

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

$$2m+2>0 m-2<0$$

The solution satisfying both inequalities is m\in \left(-1,2\right).

$$m\in \left(-1,2\right)$$

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

$$m-2>0 2m+2<0$$

This is false for any m.

$$m\in \emptyset$$

The final solution is the union of the obtained solutions.

$$m\in \left(-1,2\right)$$