Solve the inequality x^2 < -8x + 9

Notice that the inequality may be rearranged to give the quadratic x^2 + 8x - 9 < 0.Factorise the quadratic to give (x-1)(x+9) < 0.Treating the expression as an equality, recall that if the product of two values is equal to zero then at least one of those values must be zero. Hence notice that the roots to the equation are 1 and -9. We are only interested in the values of the quadratic below zero, check if the parts of the quadratic below x=0 are converging or diverging.Since the two ends of the line are converging the solution must be -9 < x < 1.It may be useful to attempt to solve the question graphically as well as numerically.