# How do you solve and write the following in interval notation: 3 < |x| – 5?

Aug 2, 2016

$- 8 > x > 8$

#### Explanation:

$8 < | x |$

Write as $8 < | \pm x |$

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$\textcolor{b l u e}{\text{Consider the case } 8 < | + x |}$

$\text{ }$ This is the same as $\textcolor{m a \ge n t a}{8 < x}$

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$\textcolor{b l u e}{\text{Consider the case } 8 < | - x |}$

$\text{ }$ This is the same as $\textcolor{g r e e n}{x < - 8}$

Example: suppose $x = - 9$ then $- 9 < - 8$ is true

Also

$| - 9 | = + 9 \text{ " ->" " 8<|x|" " ->" " 8<|-9|" " ->" } 8 < 9$
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$\textcolor{b l u e}{\text{Putting it all together}}$

color(blue)(color(magenta)(8 <) x color(green)(< -8)

Which is the same as: $- 8 > x > 8$

The open dots mean that x does not assume those values

So we have combined: $x < - 8 \text{ and } x > 8$