Real objects never feel one force at a time. The push fights friction; the cable fights the weight. Newton's second law only listens to the net force — the arrows summed, winners minus losers — so the working order is always: net the forces FIRST, then hand Newton the leftover. Feed $F = ma$ a gross force and it will cheerfully hand you a wrong answer with perfect arithmetic.

And keep the estimate-first habit from last chapter: one order-of-magnitude guess before computing. A hand-pushed cart lives near $1\ \mathrm{m/s^2}$; free fall is ten; a hundred is machinery you would not stand near. Five seconds of guessing catches almost every added-instead-of-subtracted slip below.