If $|x-2| \geq |x-4|$ then $x \in \ldots$

Solve the given inequality for real $x$: $\frac{x}{3} > \frac{x}{2} + 1$

Solve the given inequality and show the graph of the solution on a number line:
$5x - 3 \geq 3x - 5$

Solve the following inequality: $\frac{2x+3}{5} - 2 < \frac{3(x-2)}{5}$

Let $a, b, c, d$ be numbers in the set $\{1, 2, 3, 4, 5, 6\}$ such that the curves $y = 2x^3 + ax + b$ and $y = 2x^3 + cx + d$ have no point in common. The maximum possible value of $(a - c)^2 + b - d$ is

Solve $5x - 3 < 7$,when $x$ is an integer.