Final answer:
The absolute value statements for the given problems express the distance between two values, such as |x - 48| for the distance between x and 48, and similar expressions for the other problems.
Step-by-step explanation:
The concept of absolute value as it relates to distance can be understood by considering absolute value as the magnitude of displacement in mathematics. To write absolute value statements as distance problems, we consider the absolute value of the difference between two quantities as the distance between them.
For part (A), the distance between x and 48 is represented as |x - 48|. This expression signifies the non-negative distance between x and 48 on a number line.
For part (B), the absolute difference between 3x² and 48 can be written as |3x² - 48|, denoting the distance between the value of 3x² and 48 with no regard to the direction.
For part (C), to find the distance between 15x and 48, we write the expression as |15x - 48|, which shows how far apart these two expressions are numerically.
Lastly, for part (D), the absolute difference between 48 and 3x is expressed as |48 - 3x|, indicating the unsigned distance between these two terms.