1.
without looking aside; single-mindedly; with total focus; without distraction
Doing something with complete concentration, without being distracted by anything else. Literally 'without even glancing to the side.' Always used in a positive sense, praising dedication and focus.
脇目も振らず走った。
I ran without looking aside.
脇目 means 'a sideways glance' and 振らず is the negative form of 振る (to turn). The expression is always used in the fixed negative form — you cannot say 脇目を振る. Functions as an adverb modifying the following verb. Commonly paired with: 走る (to run), 働く (to work), 勉強する (to study), 進む (to advance). Conveys admiration for intense dedication.