In Exercises 51–60, rewrite each expression without absolute value bars. |7 - π|

Key Concepts

Absolute Value

Absolute value is a mathematical function that measures the distance of a number from zero on the number line, regardless of direction. For any real number x, the absolute value is denoted as |x| and is defined as |x| = x if x ≥ 0, and |x| = -x if x < 0. This concept is crucial for understanding how to rewrite expressions that involve absolute values.

Piecewise Functions

A piecewise function is a function defined by multiple sub-functions, each applying to a certain interval of the main function's domain. When rewriting expressions involving absolute values, it is often useful to express them as piecewise functions, which clearly delineate the conditions under which each part of the function applies. This helps in understanding how to handle different cases based on the input value.

Inequalities

Inequalities are mathematical statements that describe the relative size or order of two values. They are essential when dealing with absolute values, as they help determine the conditions under which the expression inside the absolute value is positive or negative. Understanding inequalities allows one to correctly rewrite expressions without absolute value bars by considering the cases where the expression is greater than or less than zero.