Modulus Graph Sketching

Please could someone explain the method used in sketching modulus graphs such as the one on Q16 in this booklet? I don't understand the method behind using intervals and why the signs next to the brackets change depending on the interval.

http://www.madasmaths.com/archive/maths_booklets/standard_topics/various/curve_sketching_exam_questions.pdf

Thanks!

When whatever is in-between the mod signs is positive or zero, you can simply remove the mod signs, as the absolute value of zero or a positive number is just that positive number. Whereas if whatever is in-between the mod signs is negative, you want the same number but positive, so you multiply by -1. So your first job is to use inequalities to figure out when x - 4 and x + 1 are greater than or equal to zero, and when they are negative. Then different intervals will yield a different, modulus-free function, hence why the function is split up in the solution.