  We study the approximability of constraint satisfaction problems (CSPs) by
linear programming (LP) relaxations. We show that for every CSP, the
approximation obtained by a basic LP relaxation, is no weaker than the
approximation obtained using relaxations given by $\Omega\left(\frac{\log
n}{\log \log n}\right)$ levels of the Sherali-Adams hierarchy on instances of
size $n$.
  It was proved by Chan et al. [FOCS 2013] that any polynomial size LP extended
formulation is no stronger than relaxations obtained by a super-constant levels
of the Sherali-Adams hierarchy.. Combining this with our result also implies
that any polynomial size LP extended formulation is no stronger than the basic
LP.
  Using our techniques, we also simplify and strengthen the result by Khot et
al. [STOC 2014] on (strong) approximation resistance for LPs. They provided a
necessary and sufficient condition under which $\Omega(\log \log n)$ levels of
the Sherali-Adams hierarchy cannot achieve an approximation better than a
random assignment. We simplify their proof and strengthen the bound to
$\Omega\left(\frac{\log n}{\log \log n}\right)$ levels.
