How do you solve and write the following in interval notation: $| x | – 2 <7$ ?

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Answer 1 · 2016-06-25T20:00:12

First of all we write

$|x|-2<7$

$|x|<9$

then we remove the absolute value remembering that we have to use both signs $\pm$ and when we use the $-$ sign we have to invert the inequality.

$|x|<9$

$x<9$ and $x> -9$

This tell us that $x$ can assume any value between $-9$ and $9$ that can be written as

$-9 < x < 9$
or
$x\in(-9,9)$ .

How do you solve and write the following in interval notation: | x | – 2 <7| x | – 2 <7?