Solve the inequality (x – (1))(x – (8)) < 0.
Note
Start by finding the critical points, because these are the values where the product becomes zero. These points divide the number line into intervals. For a product of two first-degree factors with positive leading coefficient, the product is positive outside the two roots and negative between them. Here, The critical points are x=1 and x=8. A product of two linear factors is positive outside the roots and negative between them. Therefore the solution is 1 < x < 8. Since the inequality is strict, the boundary points themselves are not included in the answer.
