MGMAT: Inequalities & Absolute Value (why did A.V. pop u

Reason why you need to use absolute values in this case is:

For any negative number, its square is +ve, eg. 5² = -5² = 25
In solving any problem, remember if x² = 25 , then x can be either +5 or -5.
Of course, in some problems, like if problem asks you to say, number of people, which can't be a -ve value, you can ignore the negative value in that case, but in other cases, be it inequality problem, or any other problem, you have to consider the negative value.

Take the case of cubes, cube of a -ve number is -ve., ie. 5³ = 125. and -5³ = -125.
So, if the above problem would've been (x+1)³<125, you dont need to use absolute value in this case.,
answer of this would be x+1<5, or x<4.

When dealing with even exponents, you have to use absolute value brackets.

Hope its clear to you.