Also, the number before a letter, called the coefficient, is an implied multiplication (which i usually write as * on the PC rather than x or the dot) of the letter. So basically, 5f = 5 times f. As Thief mentioned, f can be any number, or even a whole equation by itself. Say, f = 5 + 5, which gives us that 5f = 5*(5 + 5), or 50. The parentheses around 5 + 5 imply that this is to be solved before doing anything else, so (5 + 5) is effectively the same as 10. I'm not actually sure what level you're at, so forgive me if i say something you already know in and out.
However, letters can also be unknowns, in which case you're generally asked to isolate the unknown. This is fairly easy with a single unknown (as long as there aren't too many log's and ^2's and square roots, but they aren't part of basic algebra as far as my limited knowledge goes). If you have an equation that is like 2x + 4x + 7 = 13, you can start out by adding the x's, so it goes like 6x + 7 = 13. To remove the +7, just subtract 7 on both sides, so that 6x + 7 - 7 = 13 - 7, which means that 6x = 6. If your next guess was to divide both sides with 6, then you're completely right, since 6x means 6 * x. So, 6x/6 = 6/6, which gives us the delightfully simple solution of x = 1. If you then put 1 in where x otherwise is, we get that 2 * 1 + 4 * 1 + 7 = 13.
Using a single letter is fairly straight forward (just do the operations on the number before the letter), though it gets a bit tricker when you involve two or more. For example, if you have x + y, you can't further shorten that without knowing what either of those mean. Something like x * y can be shortened to xy, and even worse, 2x * 3y becomes 6xy. If you didn't know already, a lacking operator (plus/minus/divide/multiply) implies multiplication, so 6xy means 6 * x * y. Multiplication can be done in any order, so don't worry too much about that. When you eventually find the values of x and/or y, just substitute that number for the symbol. Say, x = 3 and y = 4, giving us that 6xy = 6 * 3 * 4 = 6 * 12 = 72.
Addition and subtraction are both simple, and multiplication isn't that bad either. Division is a smidge harder, however, since there are a few oddities to take note of. Using (x + y)/x as an example, we can split that one up into two divisions; x/x + y/x. Since a number divided by itself equals 1, that gives us 1 + y/x. If we say that 1 + y/x = 8, we then get that 1 + y/x - 1 = 8 - 1, and thus, y/x = 7. Multiplying a division by the divisor neutralizes said component, so y/x * x = 7 * x, and thus y = 7x. To make anything out of that, you need a second equation, so let's say y/2 + x = 3. We know that y = 7x, so we can insert that, giving us 7x/2 + x = 3. So, we divide 7x by 2, which is pretty easy; 3,5x. Then we get 3,5x + x = 3, and 4,5x = 3. Which is a pretty horrible number, but regardless, to find x, we divide 3 by 4,5, which is the coefficient of x. 3/4,5 = 0,667, so x = 0,667. We can then find out that y = 7 * 0,667, which is equal to 4,667. Insert these numbers into the original equation, (x + y)/x, and we get (4,667 + 0,667)/0,667 = 8.
tl;dr terrible crash course in basic algebra
Sorry guys but sometimes it's nice to ramble about basic algebra after all that college level calculus. :c
Author
Topic: Urgent help with basic algebra and its symbols. (Read 3166 times)