When 4 times a number is subtracted from 5, the absolute value of the difference is at most 13. Use interval notation to express the set of all numbers that satisfy this condition.

Absolute value measures the distance of a number from zero on the number line, regardless of direction. It is denoted as |x|, where |x| = x if x is positive or zero, and |x| = -x if x is negative. In this problem, the absolute value indicates that the difference between 5 and 4 times a number can vary within a specific range.

Inequalities express a relationship where one quantity is larger or smaller than another. In this case, the condition states that the absolute value of the difference must be at most 13, which translates to a double inequality. Understanding how to manipulate and solve inequalities is crucial for finding the solution set.

Interval notation is a mathematical notation used to represent a range of values. It uses parentheses and brackets to indicate whether endpoints are included (closed interval) or excluded (open interval). In this problem, once the solution set is determined, interval notation will succinctly express all numbers that satisfy the given condition.