Word Problem #1:
You are in a submarine at a depth of some unknown value x. The submarine rises 15 feet. After this point, you are able to record the depth to be 18 feet below sea level.
x = original depth
15 = height you rise up
-18 = final depth
x+15 = final depth
x+15 = -18 is the equation we solve to find the value of x
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Word Problem #2:
You are in debt to your friend. Debt is represented by negative numbers. For example, writing -2 means you are 2 dollars in debt. If you start off being x dollars in debt, but pay off $15, then you will have a balance of x+15 dollars. If this new final balance is -18, then we can say x+15 = -18
So in short: you go from x dollars in debt to 18 dollars in debt after paying off $15 to your friend.