Question

Write an absolute value inequality that represents all real numbers x that are at most 3 units away from 6

Answer 1

We need to create an inequality that represents the interval that goes from 3 units to the left of 6 and 3 units to the right of 6. This means that the interval will go from:

$\begin{gathered} 6-3=3 \\ 6+3=9 \end{gathered}$

The absolute value is an operator that returns the value of a number without its sign. With this in mind:

$|x-6|\text{ <3 }$