# How do you solve 4 - |3k+1| <2?

Apr 26, 2017

$k < - 1$
$k > \frac{1}{3}$

#### Explanation:

To make the absolute positive multiply everything by (-1). Note that this turns the inequality sign round the other way. So now we have:

$- 4 + | 3 k + 1 | > - 2$

$| 3 k + 1 | > + 2$

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There are what I will call 'trigger' values that this condition relates to.

Lets determine these 'trigger' values.

Set $| 3 k + 1 | = 2$ this is the same as $| \pm 2 | = 2$

So the 'trigger' values are such that
$3 k + 1 = - 2 \text{ "=>" } k = - \frac{3}{3} = - 1$
$3 k + 1 = + 2 \text{ "=>" } k = \frac{1}{3}$

so we have $| \text{increasingly negative} | > 2 \implies k < - 1$

and we have $| \text{increasingly positive} | > 2 \implies k > \frac{1}{3}$