Prove that there is a positive constant c so that every set A of n nonzero reals

contains a subset B C Aofsize|B| > cn so that there are no b_1,b_2,b_3, b_4 belong to B

satisfying

b_1 + 2b_2 = 2b_3 + 2b_4 .

contains a subset B C Aofsize|B| > cn so that there are no b_1,b_2,b_3, b_4 belong to B

satisfying

b_1 + 2b_2 = 2b_3 + 2b_4 .