Actually, the way to solve this kind of inequation is to determine the crucial points at which the sign of every absolute flips from negative to positive.
Following this rule, we have only 1 crucial point : x = -3/2.
So, we have 2 domains to study : x < -3/2 and x >= 3/2. Each domain gives 1 simplified inequation.
In your case, the inequation 1 is affected to x < -3/2. As well, the inequation 2 is related to x >= 3/2.
But, your last inequation is not linked to any domain. Indeed, it never represents the original inequation (flip of sign + minus).