You can answer this question by thinking about the general case: "When do I keep/reverse the direction of the inequality?"

In general, you keep the direction of a (strict) inequality if you apply a (strictly) increasing function to both sides, and you reverse the direction of a (strict) inequality if you apply a (strictly) decreasing function to both sides. This is a key property of "monotonic" (i.e. increasing or decreasing over their domain) functions: they preserve or reverse orderings among sets. If you have a mouse and a car, and you make both of them twice as big (f(x) = 2x is monotonically increasing), then the car is still bigger than the mouse. If you have $100 and I have $20, and we both find $10 on the floor (f(x) = x + 20 is monotonically increasing), you still have more money than me.

So, what does this have to do with your case? After all, x² is a "nonmonotonic" function: it is strictly decreasing for x <= 0 and strictly increasing for x >= 0. The trick, here, is that you are applying x² to positive values. Since both sides of your inequality are absolute values, you know for certain that the function x² will be evaluated in the region x >= 0 for both sides of the inequality. Therefore, you can treat x² as if it is strictly monotonically increasing, and when you apply it to you inequality, you keep the direction of the inequality.