If income effect and own substitution effect of this price change work in the opposite direction, then the good x is necessarily a normal good.

If income effect and own substitution effect of this price change work in the opposite direction, then the good x is necessarily a Giffen good.

If income effect and own substitution effect of this price change work in the same direction, then the good x is necessarily inferior.

If income effect and own substitution effect of this price change work in the same direction, then the good x is necessarily an ordinary good.