Rewrite each expression without absolute value bars. |12 - π|

Verified step by step guidance

1. Recall that the absolute value of a number \(x\), denoted \(|x|\), is defined as \(x\) if \(x \geq 0\), and \(-x\) if \(x < 0\).
2. Identify the expression inside the absolute value bars: \(12 - \pi\).
3. Determine whether \(12 - \pi\) is positive or negative by comparing the values of 12 and \(\pi\) (approximately 3.14).
4. Since \(12 - \pi\) is positive (because 12 is greater than \(\pi\)), the absolute value expression \(|12 - \pi|\) is equal to \(12 - \pi\) without the absolute value bars.
5. Therefore, rewrite \(|12 - \pi|\) as \(12 - \pi\).

Key Concepts

Absolute Value Definition

The absolute value of a number represents its distance from zero on the number line, always as a non-negative value. For any real number x, |x| equals x if x is positive or zero, and -x if x is negative.

Evaluating Expressions Inside Absolute Value

To rewrite an expression without absolute value bars, first evaluate or analyze the expression inside. Determine whether the expression is positive, negative, or zero to decide how to remove the absolute value correctly.

Properties of π (Pi) in Algebraic Expressions

π is an irrational constant approximately equal to 3.14159. Understanding its approximate value helps compare and simplify expressions involving π, such as determining the sign of 12 - π for rewriting absolute values.