# inequalities – Verification of inequality

I want to check an inequality in mathematica but I do not know where I was wrong. Please help me, thanks in advance.

$$psi (t): to[0infty)[0infty)[0infty)[0infty)$$ and $$phi (t): to[0infty)[0infty)[0infty)[0infty)$$

or;

$$psi (t) = 3/2 * t ^ 2$$ and $$phi (t) = t$$

$$d (x, y) = | x-y |$$ or $$x, y epsilon mathbb {R}$$

The above are the conditions that I want to put on the given inequality

$$begin {equation} 3 * t ^ 2 * d (x, y) -3 / 2 * t ^ 2 * d (x, y)] leq (3/2 * t ^ 2 * d (x, y)) ^ alpha * (t * d (x, y)) ^ {1- alpha} end {equation}$$
or $$alpha epsilon (0,1)$$