Question

How do I write this in interval notation?
6 lxl < 1

Answer 1

first I would solve the inequality for x

Answer 2

|x|< 1/6
since |x| > 0 then
-1/6< x < 1/6 or
x in (-1/6,1/6)

Answer 3

\[
6|x| < 1 \implies |x|<\frac 16
\]This leads to two equations: \[
x<\frac 16,\quad -x<\frac 16\implies x>-\frac 16
\]Combine them to get: \[
-\frac 16<x<\frac 16
\]The \(<\) becomes \((\), while \(\leq \) becomes \([\).
The same logic applies to \(>\) and \(\geq\).
Our interval is \((-1/6,1/6)\).
We can say \(x\in(-1/6,1/6)\) to say that \(x\) is within the interval.