For that same inferior good, a fall in its price also raises the consumer's real income. Because the good is inferior, this income effect on its own causes quantity demanded to

For an inferior good, a rise in real income lowers quantity demanded on its own, so the income effect pulls in the opposite direction to the substitution effect. For an ordinary inferior good the substitution effect is the larger of the two, so quantity demanded still rises overall, just by less than for a normal good; only in the extreme Giffen case does the income effect win outright.