How do you solve absx - 4 =3x?

Jul 6, 2015

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

Explanation:

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

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

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