Question 689205: -12x+36=6x-24-4
How do determine when to use a - or + for this final answer I got 9/32 but is it a - or +
Answer by KMST(5328)   (Show Source):
You can put this solution on YOUR website! Sorry, you were wrong, but I hope I can help. Math should not be scary, and you should be able to solve equations by using your own common sense, without memorizing rules and recipes.
THE SOLUTION:
You start with 
You may decide to add 24 and 4 to both sides of the equality to get a friendlier equivalent equation:
 <--> 
Then, you may decide to add 12x to both sides of the equality:
 --> 
At this point, it would make sense to divide both sides of the equality by 18:
 --> 
Then you would like to simplify the fraction and write the answer starting with the x, as
THE STRATEGY:
To solve equations like that one, you carefully transform the equation into equivalent equations until you get to the solution.
The trick is to keep transforming the equation so as to make it easier each time. Just like for solving a puzzle, or unraveling a badly knotted string, or navigating a maze, you need to stay calm and think to chose your next step so as to go in the right direction.
THE CONCEPT:
In an equation you have two mathematical expressions (one on each side of the equal sign).
The equation is a statement that says that those two expressions are equal.
If you add to both sides (or subtract from both sides) the same number or the same expression, you get a new equation with two sides that are still equal.
If the original equation was true, so will be the new one (and vice versa).
It also works backwards, because you can go back (subtract instead of adding, for example).
That's why we say that the old equation, and the new, transformed equation are equivalent.
If the new equation is simpler/easier, you got closer to the solution.
If you multiply both sides (or divide both sides) by a same number that is not zero, you get a new equivalent equation with two sides that are still equal (and vice versa). You cannot divide by zero, and if you multiply both sides of an equation by zero, you get 0=0, which is always true, even if the original equation had been not true.
Multiplying and dividing by expressions is trickier, because any expressions could be zero for some value of x.
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