Solve the following inequality: x^2 + x -12<0
Firstly we have to factorize the quadratic. We do this by finding two numbers that multiply to -12 and add to 1.Looking at the factors of 12 we can see that x2+x-12= (x-3)(x+4)because -3 x 4 = 12 and 4-3=1. Now we can draw a graph to help us solve this inequality. We know the graph cut the x-axis at 3 and -4 because that is when the brackets equal 0. Finally we can shade the section of the graph where y<0 and this will help us write our inequality answer of:-4<x<3
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