I don't understand when to use "hard brackets" or "soft brackets."

⚑ Flag

You use hard brackets when the number is part of the solution, and use soft brackets otherwise. Other way to put it would be to use the hard brackets when your inequality is "greater than or equal to" or "less than or equal to," and use the soft ones when you just have "greater than" or "less than." You must be careful, because sometimes the intersection segment might have one of each on its extremes (so you'll have one hard and one soft).