Solve 2(x-7)x<0

$$2 ( x - 7 ) x < 0$$

Solve for x

$$x\in \left(0,7\right)$$

Solution Steps

Use the distributive property to multiply 2 by x-7.

$$\left(2x-14\right)x<0$$

Use the distributive property to multiply 2x-14 by x.

$$2x^{2}-14x<0$$

Factor out x.

$$2x\left(x-7\right)<0$$

For the product to be negative, x and x-7 have to be of the opposite signs. Consider the case when x is positive and x-7 is negative.

$$x>0 x-7<0$$

The solution satisfying both inequalities is x\in \left(0,7\right).

$$x\in \left(0,7\right)$$

Consider the case when x-7 is positive and x is negative.

$$x-7>0 x<0$$

This is false for any x.

$$x\in \emptyset$$

The final solution is the union of the obtained solutions.

$$x\in \left(0,7\right)$$