So in my Destiny career, I've heard the phrase "pop a synth" plenty of times, but occasionally back then (and very often recently), I've been hearing a lot of random players say "eat a synth".
Now, I don't know exactly what you do with ammo synthesis (plural form of synthesis?), but I don't think you EAT them.
I've been hearing so much (usually from younger sounding players):
"Gonna eat a synth"
"One sec, eating heavy ammo"
"Cover me, gonna eat a heavy synthesis"
But IDK, maybe I'm wrong.
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Only time I've known something to eat a synth is after I've used one and proceeded to shove my shotgun into the enemies mouth.