MWG_3D4_C, why the solution seems in reverse?

I’m doing exercises of Chapter3 of MWG, there’s a problem that I don’t understand (I didn’t figure out the solution manual either…).

It is about exercise 3.D.4, the full statement of the exercise is as follows:

Let $(−∞,∞)×R^{(L−1)}_+$ denote the consumption set, and assume that preferences are strictly convex and quasilinear. Normalize $p_1=1$.

(a) Show that the Walrasian demand functions for goods $2,…,L$ are independent of wealth. What does this imply about the wealth effect of demand for good 1?

(b) Argue that the indirect utility function can be written in the form $v(p,w)=w+phi(p)$ for some function $phi(⋅)$.

(c) Suppose, for simplicity, that $L=2$, and write the consumer’s utility function as $u(x_1,x_2)=x_1+η(x_2)$. Now, however, let the consumption set be $R^2_+$, so that there is a nonnegative constraint on the consumption of the numeraire $x_1$. Fix prices $p$, and examine how the consumer’s Walrasian demand changes as wealth w vary. When is the nonnegativity constraint on the numeraire irrelevant?

Question In the solution in part c we reach to the conclusion that the consumer spends all the wealth on $x_2$ and spend what’s left on $x_1$. Shouldn’t this be in reverse?

p.s. I’m thinking about the graph that maximum utility is achieved when we spend all the money on good 1 on nothing on good 2.