### Home > A2C > Chapter 4 > Lesson 4.2.3 > Problem 4-105

Think of absolute value as a statement about distance as you answer the questions below. What values of in parts (a) through (d) make each equation true?

What numbers are a distance of

from 7? Picture this on a number line. ,

See part (a).

See part (a).

See part (a)

Remember absolute values cannot be negative.

What mathematical operation is best used for calculating the distance between two numbers? In other words, if you want to know the distance from

to , what arithmetic expression represents that distance? Subtraction,

Suppose you want to write an equation to represent the statement, “The distance between a number and

is .” You would not know whether to write or. Absolute value equations can allow you to write a correct expression without knowing which value is larger. Write two absolute value equations that mean “the distance between a number and is .” Write and solve an absolute value equation that says each of the following:

See the answer to part (f).

*“The distance between*and is .”

or *“The distance between*and is .”