Algebra 101 - Quick Question

[Matt_Ramsden]

Just a quick question on the

-100 = -2t

I fully understand why we divided by -2. However as I was watching my mind initially went to +2t to come to zero and then do the same on the other side quickly concluding to t = 98 (and seconds later realising that I was utterly wrong).

So just to clear up why I thought that, was that because that would only apply to a number without a variable attached to it (and then doing the same on the other side); as doing +2t would bring me to 0 leaving me with no t at all, and +98 on the other side in the next step would also leave me with 0 because t on its own equals 1t?

[garypettie]

Hi @Matt_Ramsden.
(-2t) is the same as saying (-2) * t, so we need to divide in order to break apart that multiplication.

If you add 2t to both sides you end up with
(2 * t) - 100 = 0
but that doesn’t really get you any closer to an answer, since you still haven’t isolated the variable. If anything, it get’s you slightly further away because you’ve added more stuff around the ‘t’ that you have to get rid of.

Remember that you always have to do the same to both sides of the equation, so there’s no way to completely remove t. Whatever you do would just end up moving it around.

[DragonBloodthirsty]

When solving a simple one-step equation (like we have here) it is helpful to identify the operation. You’ve got four basic operations like you find on a four-function calculator (add + , subtract - , multiply * , and divide / ). In this case, your -2t has multiplication, so you’ll need to apply division.

You might just need to practice until your brain stops making mistakes.