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.

Key Concepts

Absolute Value

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 be both positive and negative, leading to two inequalities to solve.

Inequalities

Inequalities express a relationship where one quantity is larger or smaller than another, using symbols like <, >, ≤, or ≥. In this context, the condition that the absolute value of the difference is at most 13 translates into two separate inequalities that need to be solved. Understanding how to manipulate and solve inequalities is crucial for finding the solution set.

Interval Notation

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 inequalities are solved, the solution set will be expressed in interval notation, providing a concise way to describe all numbers that satisfy the given condition.