Question

write an absoolute value inequality that represents, "all real numbers less than 4 units from 6 on a number line."

Answer 1

The question is asking for an absolute value inequality that represents all real numbers less than $4$ units from $6$ in any direction on the number line.

This can be written as $2 \ \textless \ |x| \ \textless \ 10$.

$4$ numbers from $6$ to the left is or $6-2$, or $4$. $4$ numbers to the right of $6$ is $6+4$, or $10$. Therefore, the inequality can only allow real numbers whose absolute values fall between $2$ and $10$.