Chapter R, Problem 1AFC

For Exercises 1-2, write an inequality using an absolute value that represents the given condition.

The distance between y and L is less than $\epsilon$ (epsilon).

To determine

The inequality use the absolute value that represents the distance between $y$ and $L$ being less than $\epsilon$(epsilon).

Answer to Problem 1AFC

Solution:

The inequality use the absolute value that represents the distance between $y$ and $L$ being less than $\epsilon$ is $\left|y-L\right|<\epsilon \text{or }\left|L-y\right|<\epsilon$.

Explanation of Solution

Given Information:

The distance between $y$ and $L$ is less than $\epsilon$(epsilon).

Consider the provided information,

The distance between two points $a$ and $b$ on a number line is absolute value of their difference.

$\left|a-b\right|\text{or }\left|b-a\right|$

So, the distance between $y$ and $L$ being less than $\epsilon$(epsilon) is given by

$\left|y-L\right|<\epsilon \text{or }\left|L-y\right|<\epsilon$