Solve (x+1)(x-5)<0}

$$( x + 1 ) ( x - 5 ) < 0 \}$$

Solve for x

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

Solution Steps

For the product to be negative, x+1 and x-5 have to be of the opposite signs. Consider the case when x+1 is positive and x-5 is negative.

$$x+1>0 x-5<0$$

The solution satisfying both inequalities is x\in \left(-1,5\right).

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

Consider the case when x-5 is positive and x+1 is negative.

$$x-5>0 x+1<0$$

This is false for any x.

$$x\in \emptyset$$

The final solution is the union of the obtained solutions.

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