The first term on the right-hand side is the substitution effect, which is always negative. The second term on the right side is the income effect, which can be positive or negative. For inferior goods, this is negative, so subtracting this means adding its positive absolute value. The non-derivative component of the income effect is a measure of a consumer's existing demand for the good, meaning that if a consumer spends a large amount of his income on an inferior good, then a price increase could cause the income effect to dominate the substitution effect. This leads to a positive partial derivative of the good's demand with regards to its price, which violates the law of demand.
