Question
Express $|3 x|<\frac{1}{3}$ in interval form.

Answer

Comparing $|3x| < \frac{1}{3}$ with $|x - a|<δ$ we get
$a = 0$ and $δ = \frac{1}{9}$.
Interval form $: N(a - δ ; a + δ)$
Putting $a = 0$ and $δ =\frac{1}{9}$.
$|3 x|<\frac{1}{3}=\left(0-\frac{1}{9} ; 0+\frac{1}{9}\right)$
$=\left(-\frac{1}{9} ; \frac{1}{9}\right)$

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