|x + 1| ≤ 27
generally, with absolute value equations/inequalities, you always want to isolate the terms between the absolute value bars, which is already taken care of here. once you have the absolute value on one side, and the rest of the inequality on the other, set it to both -27 and 27, then solve it like a normal two-step equation. however, for the one set to the -27 in this problem, you have to flip the sign of your inequality:
x + 1 ≥ -27
x ≥ -28
and
x + 1 ≤ 27
x ≤ 26
the reason you set it to both -27 and 27 itself is because of the definition of absolute value: it's just a number that says how many units something is away from 0 on a number line. so, if something is 27 units away, it could be 27 units in the positive direction or 27 units in the negative direction. you have to set it equal to both so you get both answers.
your answer in interval notation is [-28, 26]
