$$ \frac{1}{3}(10x-7)>x $$
Multiply both sides by 3 and combine like terms:
$$ 10x-7>3x$$
$$ 7x-7>0$$
Solving for \(x\)
$$ 7x>7$$
$$ x>1$$
Only \(\boxed{3}\) satisfies this inequality.
We can plug in the answer choices. Start with an intermediate value (2nd or 3rd choice) and move up or down accordingly.
For these types of inequality questions, a good idea would be to use the smallest and largest number. In this case, the largest number \( \boxed{3} \) works.
$$ \frac{1}{3}(10x-7)>x $$
$$ \frac{1}{3}(10(3)-7)>3 $$
$$ \frac{1}{3}(23)>3 $$
$$ \frac{23}{3}>\frac{9}{3} \checkmark$$