Find the set of values for which x^2 - 7x - 18 >0

To see where the graph is greater than zero, we start by finding where it meets zero. By factorising (x^2 - 7x - 18), we find it equals (x-9)(x+2). The expression equals zero at the points x = 9 and x = -2. Now we need to know the shape of the graph. First, we can see the x^2 term is positive, which means the curve is a 'bowl' shape. Alternatively, we can work out if an x value in between -2 and 9 works for the inequality. Say x=0. 0^2 - 7(0) - 18 = -18. This is less than 0 so does not satisfy the inequality. Now we know the graph is more than zero outside of the interval between x=-2 and x=9. Therefore x < -2 or x > 9.