I went over my Algebra worksheet today, and realized since it's been years since I've even looked at a math problem (top that off with never giving a shit about math) I have completely forgotten everything outside of basic arithmetic. Yes, I am an idiot.
So, I finally sat down and figured out the little shits that have been bothering me.
My most common mistakes:
1) Here's a note that I made either on accident, or I simply don't understand. I remembered the professor telling us that the negatives cancel out in the fraction (-25/-10). Is that because anytime there is a negative sign in front of an integer, it really equates to -1, for instance, -25 could also be written as (-1)25? I'm not sure. I would have simplified (-25/-10) to (-5/-2). I guess what I said makes sense. I'm hoping I am right.
2) Order of operations. Thought I knew them, with that whole "Please Excuse My Dear Aunt Sally" thing, but apparently, I am in fact still an idiot. For instance, I had no idea that the parentheses had to be completely removed before you could go on to do other things to the problem. In 12-4(5-7)^2, I kept getting 32 over and over again. That was because I did it like this:
12-4(5-7)^2
12-4(-2)^2
12-4(4)
8(4) = 32
I have been missing so many math problems for SO MANY YEARS because I have always messed that up.
Correct solution (second half):
12-4(4)
12-16 = -4
I feel so dumb sometimes!
3) So, apparently, if you have a negative sign on the outside of parentheses, it, like, changes the signs in within that parentheses, or something. Once again, I am kicking myself for not giving a shit in high school. I missed a super simple problem several times because I was completely oblivious to how this rule worked.
Example:
4(2x+3) - (5x-2) = 4(3x-7)
Distribute
8x + 12 - 5x + 2 = 12x - 28 (Yeah, I had no idea. I am a dumbass)
Combine the terms, and voila. Final answer is (14/3).
4) Clearing fractions. Holy hell, I have always hated fractions. To me, they might as well be Latin. Then, I finally took the time to just understand them, and realized I now love them. Super easy!
Example:
(4/5)x + 2 = (3/5)x - 7
So, I learned a totally new and awesome trick to get rid of those fractions, last class. Find the lowest common denominator, and apply it to the whole problem. Voila!
[5(4/5)x + 2 = (3/5)x - 7]
Distribute the multiplier 5 throughout the whole problem. It cancels out the denominators, so you're left with 4x on one side and 3x on the other.
4x + 10 = 3x - 35
And now the problem is easy!
5) Graphing inequalities. Blech.
This one still kind of gives me a headache, but I think I got it under control.
X is > or = to 1: [1, infinity) ___1__>
The only way I can even begin to try to explain this is look at what the lowest possible number could be. That number goes on the left. Since X could be either 1 or any number bigger than 1, it goes on until infinity, with no definition. Since 1 is defined, I used a bracket, and since infinity is undefined, I used a parentheses.
And at this point I am mathed out. Might have to move onto some other boring shit.
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