Let us consider a linear equation (∗) a1x1 + . . .+ akxk = b, where a1, . . . , ak, b ∈ Z. We call the equation (∗) invariant if both s = a1 + . . .+ ak = 0 and b = 0, and noninvariant otherwise. We say that a set A is (∗)-free if it contains no nontrivial solution to (∗) and define r(n) as the size of the largest (∗)-free set contained in [n] = {1, . . . , n}. The behavior of r(n) has been extensively studied for many cases of invariant linear equations. The two best known examples are the equation x + y = 2z, when r(n) is the size of the largest set without arithmetic progression of length three contained in [n] (see [6]), and the equation x1 + x2 = y1 + y2, when r(n) becomes the size of the largest Sidon subset of [n] (see [3], [7], [8]). Much less is known about the behavior of r(n) for noninvariant linear equations, maybe apart from sum-free sets (see for example [1], [2], [5], [10]). The main contribution to this subject was made by Ruzsa [9] who studied properties of sets without solutions to a fixed noninvariant linear equation. Following his paper let us define Λ(∗) = sup{d(A) : A ⊆ N, A is (∗)-free}, Λ(∗) = sup{d(A) : A ⊆ N, A is (∗)-free}, λ(∗) = lim sup n→∞ r(n)/n,