For which values of x is the following inequality satsified: x^2 + 6x + 6 < 1

(I assume I can use the whiteboard in an actual lesson/interview)

So this question might seem quite simple, and maybe it is, but this type of question can catch many students out. The first step is always to move the numbers/constants to one side which will give us a nice and easy quadratic to solve. We subtract one from both sides and the result is: x² + 6x + 5 < 0. We can then factorise the quadratic as normal to get: (x+5) (x+1) < 0. So we know that the values x = -5 and x = -1 are important values here, by solving  x + 5 = 0, and  x + 1 = 0. The next step is to draw the graph of (y = ) x² + 6x + 5, and to label the points where the graph crosses the x axis, as this is where x² + 6x + 5 EQUALS 0. But, we want the values for when x² + 6x + 5 is less than 0, and by drawing the graph, we can see it is between the two values of x = - 5 and x = -1. So in this case, being careful of which inequality sign to use, the answer is  - 5 < x < - 1. 

It is very important that you sketch a graph before answering the question at the end. Some questions will trick you out, and as the questions become more advanced, you will need the graph anyway, so it's a good habit to get into.