We cannot go any further after this point. The result of any absolute value is never negative. The absolute value represents distance from some number to 0. For example, saying |-7| = 7 means -7 is seven units away from 0 on a number line. Negative distance does not make sense.
So going back to |x-1| = -3 makes no sense as well. There are no numbers we can plug in for x to have |x-1| = -3 be true.
The equation |x-1| = -3 has no solutions, so the original equation doesn't have any solutions either.
3 sin x + 5 cos x = 0 3 sin x = - 5 cos x /: cos x ( divide both sides by cos x ) 3 sin x / cos x = - 5 3 tan x = - 5 tan x = -5/3 x = arc tan (-5/3) x ≈ - 59.036°
