How would you solve the inequality x^2-2x-8 >= 0?

We are looking for all the x values for which this equation holds. We know how to solve quadratic equations without the inequalities, and that is the first step here! So let's forget about the greater than part and imagine the equation is x^2-2x-8=0. What are the solutions? We can factorise this into (x-4)(x+2)=0. So our solutions are therefore x = -2 and x = 4.Now is where the inequality part comes in. If we draw out a generic quadratic graph with a positive x squared term which crosses the x axis as -2 and 4 (because these are our roots), then we can see that the parts of the graph which are greater than or equal to zero are to the left of and including -2 and to the right of and including -4. So the x values for which this equation is greater than or equal to zero is x <= -2 and x>= 4.