The question is asking for an absolute value inequality that represents all real numbers less than [tex]4[/tex] units from [tex]6[/tex] in any direction on the number line.
This can be written as [tex]2 \ \textless \ |x| \ \textless \ 10[/tex].
[tex]4[/tex] numbers from [tex]6[/tex] to the left is or [tex]6-2[/tex], or [tex]4[/tex]. [tex]4[/tex] numbers to the right of [tex]6[/tex] is [tex]6+4[/tex], or [tex]10[/tex]. Therefore, the inequality can only allow real numbers whose absolute values fall between [tex]2[/tex] and [tex]10[/tex].
