Confusion with a function transformation I got a HW problem wrong in my Signals and Systems class and am hoping someone can help me understand why. 
There's a discrete-time signal x[n] = u[n] + 2u[n-3] - 3u[n-6], where u[n] is the discrete-time unit step. The problem said to first draw this function, then draw the function transformation x[4n+1]. 
I drew the original function x[n] correctly, but got the transformation x[4n+1] wrong. I thought I should follow the order of operations, so first I compressed the signal by 4, and then I shifted it to the left by 1. Apparently I was supposed to shift it first, then compress it to get the correct answer. So my question is, why does this not follow the order of operations?

If you write $x[4n+1] = x\left[4\left(n+\frac{1}{4}\right)\right]$, you would see more clearly which is the correct sequence of operations.
To better understand this, let $y_1[n] = \mathcal{T}_1\{x[n]\} = x[4n]$ be the output of a system that downsamples its input by a factor of 4, and $y_2[n] = \mathcal{T}_2\{x[n]\}=x[n+1]$ be the output of a system that advance its input by 1. So, if we enter $x[n]$ to $\mathcal{T}_1$, we get $y_1[n] = x[4n]$, and if we then enter $y_1[n]$ to $\mathcal{T}_2$, then we get $y_2[n] = y_1[n+1] = x[4(n+1)] = x[4n+4]$.
