6) Sam bought 9 new baseball trading cards to add to his collection. The next day his dog ate half of his collection. There are now only 46 cards left.
How many cards did Sam start with ?

Explanation:

x = starting amount of cards

x+9 = adding nine cards to the original amount

(x+9)/2 = cutting that previous amount in half

(x+9)/2 = 46 since Sam ends up with 46 cards.

Let's solve for x. We'll undo PEMDAS in reverse to isolate the variable. So we'll start off by undoing the "divide by 2" to multiply both sides by 2. Then we'll undo the plus 9 by subtracting 9 from both sides.

(x+9)/2 = 46

x+9 = 2*46

x+9 = 92

x = 92-9

x = 83

Sam started off with 83 cards. Adding on 9 gets him 83+9 = 92, which cuts in half to 92/2 = 46. The answer is confirmed.