How to use c-gap problems to prove inapproximability?
One way to show that there is no polynomial time approximation algorithm with ratio $c$ for a certain problem X (assuming P≠NP) is to give a reduction $f$ from an NP-hard problem Y to X such that:


If $x$ is a Yes instance then the optimal value for X is at least $\beta(x)$, where $\beta(x)$ can be computed from $x$ in polynomial time.
If $x$ is a No instance then the optimal value for $X$ is less than $c\beta(x)$ (for the same $\beta(x)$).


Any approximation algorithm for X whose approximation ratio is $c$ can be used to solve Y via the reduction $f$. Therefore, there cannot be any such efficient approximation algorithm unless P=NP.

I'll let you figure out the proof of these two statements.