Modulus Inequality Question

You could have checked your answer by subbing a value like x=0 into the original inequality, but your working look ok until the end. Ive have multiplied through by -1 and solved >= 0. Your quadratic is a "n" which is <= 0, so it must be the two tails.

Not sure how you concluded the middle section?

So I went wrong because I didn't multiply by -1?

No your reasoning (whatever it was) was wrong, but the reasoning may have been easier if youd had a "u" quadratic (positive x^2 coefficient).

Sorry but I'm still quite confused because all I did was rearrange the expression after I expanded the brackets

Your penultimate line (last but one) is correct. How did you then conclude that the answer was between the two roots, rather than either side of them?

I thought that because of the inequality sign '<'

Something like this

I always thought that if you had a quadratic<0, then you would look at the inside region so would use '≤x≤'
So this part of my reasoning is wrong?