Solve 3x-7/1-x>0

$$\frac { 3 x - 7 } { 1 - x } > 0$$

Solve for x

$$x\in \left(1,\frac{7}{3}\right)$$

Solution Steps

For the quotient to be positive, 3x-7 and 1-x have to be both negative or both positive. Consider the case when 3x-7 and 1-x are both negative.

$$3x-7<0 1-x<0$$

The solution satisfying both inequalities is x\in \left(1,\frac{7}{3}\right).

$$x\in \left(1,\frac{7}{3}\right)$$

Consider the case when 3x-7 and 1-x are both positive.

$$1-x>0 3x-7>0$$

This is false for any x.

$$x\in \emptyset$$

The final solution is the union of the obtained solutions.

$$x\in \left(1,\frac{7}{3}\right)$$