People have a hang-up over negatives, but really there's no need to panic. After all if the temperature goes down to -2 it just means 2 degrees below zero. You can see this on a thermometer and everyone understands what it means, no problem. Just because negatives show up in mathematical and algebraic expressions is no big deal either. Back to your problem. To solve the equation and find t we need to gather together the unknowns (in this case the variable t) and the knowns, which are just numbers. We need to have the knowns on one side of the equals and the unknowns on the other side for this type of equation. It doesn't matter which side is used for what, although most people feel happier with the unknown(s) on the left and plain numbers on the right. We don't want loads of negatives so what we'll do is take the t's over to the right. When you cross from side of equals to the other, plus changes to minus and minus to plus. Divide changes to multiply and multiply changes to divide. Bring the -t from the left to right and it becomes +t or just t, added to the t already there makes 2t. Now bring the -19 from right to left where it becomes +19, added to the 5 already there makes 24. So we have 24=2t or put another way 2t=24. Take 2 from the left where it's multiplying over to the right where it divides into 24, making 12. So t=12. Bingo!
