How do you solve $absx - 4 =3x$ ?

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Answer 1 · 2015-07-06T23:33:27

There are two possible solutions, depending on whether $x$ is positive or not.

$x>=0$
Then the equation turns into:
$x-4=3x->-4=2x->x=-2$
This in contrary to the $x>=0$ condition, so this solution has to be discarded.

$x<0$
The sign for x is reversed, and the equation becomes:
$-x-4=3x->-4=4x->x=-1$
And this is acceptable.
Check: $|-1|-4=3*(-1)->1-4=-3$

Conclusion:
The only solution: $x=-1$

How do you solve absx - 4 =3xabsx - 4 =3x?