How do I solve x^2 > 6 - x
To solve this question we want to find the range of values that x can be to make the statement true. First we must treat it like a normal quadratic equation and move all of the values onto one side like so: x2 + x - 6 > 0. Next we want to factorise the left hand side to get: (x + 3)(x - 2) > 0.The best thing to do here is to draw the graph of y = (x + 3)(x - 2), to do this it we know it has a positive quadratic shape and at y = 0 (where it crosses the x-axis) x = -3 or x = 2. Now we want all the values of x when y = (x + 3)(x - 2) > 0 so effectively where the graph is above the x-axis. We can see from the graph that the outer values of x are positive and so we can say:x < -3 or x > 2
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