Solve the inequality: x^2 - x < 12
Firstly, the equation should be rearranged to get all the non-zero terms onto one side, with the simplest way of doing this being subtracting 12 from both sides, giving the equation x2 - x - 12 < 0. Then the next step would be to factorise the equation to find the roots of the equation, which in other words will be where the quadratic intercepts the x-axis or the line y=0. Doing this gives (x+3)(x-4) < 0, meaning the roots are the equation are x = -3 or x = 4.Now as the roots have been found, we need to find where the graph x2 - x - 12 is lower than 0 as the equality requires. The best way of doing this to be able to understand it is by drawing a graph, but if we think about what the graph will look like, we realise that as the graph is a quadratic, it will be a curved parabola with an intercept of -12 when x = 0 (test this by subbing 0 into the equation). Then we can assume that as the graph is below the line y = 0 when x = 0, and the graph crosses the line y = 0 when x = -3 and x = 4, the graph must be negative for between these values. Therefore the inequality is solved with -3 < x < 4.
