Determine whether each statement is true or false. |8-12| = |8| - |12|

Key Concepts

Absolute Value

The absolute value of a number is its distance from zero on the number line, regardless of direction. It is denoted by vertical bars, such as |x|, and is always non-negative. For example, |5| = 5 and |-5| = 5. Understanding absolute value is crucial for evaluating expressions that involve both positive and negative numbers.

Properties of Absolute Value

One important property of absolute values is that |a - b| is not necessarily equal to |a| - |b|. Instead, |a - b| represents the distance between a and b, while |a| - |b| calculates the difference of their absolute values. This distinction is essential for correctly interpreting and solving problems involving absolute values.

Evaluating Expressions

To evaluate expressions involving absolute values, one must first compute the absolute values of the individual terms before performing any arithmetic operations. In the given statement, |8| = 8 and |12| = 12, leading to the evaluation of |8 - 12|, which equals 4. This process highlights the importance of following the correct order of operations in algebra.