I agree with the person who said it's incredibly important to understand the fundamental concepts of algebra first and foremost - that's how you know which approach to take, and what to do when you don't know of a correct approach.
So, the basics of algebra are roughly:
-Making an identical change to two equal things leaves them equal, but of different value. 5+x = 10 is exactly the same as (5+x)-5 = 10-5.
-Calculating equations, even partially, does not change the value of an equation. For example, for (5+x)-5, you can subtract the five from the five, getting 0+x or simply "x".
-As long as as you apply operations that are equal and opposite, you will not change the value of an equation - but make sure you actually understand your operations! If you have "x", this has exactly the same value as 2*(x/2), 5+x-5, or x+x-x. Not all operations have an inverse that is as equal and opposite as they seem at first glance, though - notably, squareroot(x squared) doesn't necessarily equal 'x', but x^2/x does, since every squareroot operation has two possible answers. -5 and 5, squared, both end up as 25. Square rooting 25 could thus result in either option - however, dividing by "x" which is definitely either -5 or 5 so we know the value won't change).
-Operations are derived from other operations. Changing the way they look doesn't change the value. x+x is the same as 2*x, and 2*x-x is 'x'.
-Any chunk of equation can be treated as a value in it's own right, so long as its a proper chunk (it doesn't violate order of operations) and stuffed into a variable, and variables can be similarly replaced by chunks of equation so long as it has the same value. You can add new equations into the system as needed to keep track of this. 2*(x+4) = 300 can be replaced by 2*y = 300 and y=x+4.
So using earlier rules, we can solve for x above. Take 2*y=300 and realize we can isolate the variable by making an identical change to both sides (with the goal of isolating the variable), and the result will still be equal. So (2*y)/2 = (300)/2. Since we can make calculations without changing the value of either side, we can write that as y=150 without changing any values. We know that y=x+4, and that y=150, so we can replace y with either chunk (we know it's equal to both) and get either 150=x+4 or x+4=150, which are obviously identical. Then we repeat - do the same thing to each side, with (x+4)-4 = 150-4, which we can then calculate, getting x=146.
Once you've got a solid base there, it's important to start understanding the relationship between different operations. This is where formulas come in! Formulas often provide convenient ways to change complex operations from one form to another without changing the value (or by making identical changes in value to both sides of the equation)
Difficulty operation conversions are where formulas become useful Note that not all formulas are particularly important. Formulas are just rules for replacement, and not all replacements are useful. This doesn't really apply to the ones you are taught though - if a formula gets a name and ends up in a textbook, it's gonna be one of the important ones. Eventually, there's also a good chance you will want to derive some formulas of your own, but those will be the simply type you don't have to bother memorizing.
Important things to remember
Not all equations can be solved exactly - but sometimes you don't need to. If you're working out distance, it doesn't matter if your result could be either 5 OR -5, because either way its 5 units away. Sometimes just knowing the subset of possible answers is enough. Sometimes just knowing the relationship between two values is enough. Knowing that x=2y might be the goal of untangling the equation (2x+42)/2 = 21+(2y^2)/(2y). Oftentimes, finding an understandable relationship is enough.
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