19 + x = 4|x - 3| + 7

12 + x = 4|x - 3|
Case 1: x - 3 >= 0 (x >= 3). 12 + x = 4(x - 3) => 12 + x = 4x - 12 => 24 = 3x => x = 8. Valid as x >= 3.
Case 2: x - 3 < 0 (x < 3). 12 + x = -4(x - 3) => 12 + x = -4x + 12 => 5x = 0 => x = 0. Valid as x < 3.
Solutions: x = 8, x = 0.