|x| + 3x = 12
x > 0:
x + 3x = 12
4x = 12
x = 12 : 4
x = 3;
x < 0:
−x + 3x = 12
2x = 12
x = 12 : 2
x = 6.

|x| − 4x = 9
x > 0:
x − 4x = 9
−3x = 9
x = 9 : −3
x = −3
x < 0:
−x − 4x = 9
−5x = 9
$x = -\frac{9}{5}$
$x = -1\frac{4}{5}$

2(x − 5) − 6|x| = −18
x > 0:
2x − 10 − 6x = −18
2x − 6x = −18 + 10
−4x = −8
x = −8 : −4
x = 2
x < 0:
2x − 10 + 6x = −18
2x + 6x = −18 + 10
8x = −8
x = −8 : 8
x = −1