Dimensional analysis simply ensures that two sides of an equation have the same dimensions. By "dimensions" I mean quantities like distance, pressure, force, time, electric charge, etc. For example, a distance can not equal a time. So, if the dimensions are wrong, the equation is wrong, but if the dimensions are right, the equation may be right or it may be wrong. Getting the dimensions right is only part of the task!
no it can't be
7-2 IS positive. You do not need an equation for it. And if it were not positive, no correct equation would show it to be positive.
The equation above is correct.
It is when an operation is wrong and you have to find the mistake and correct and get the right answer
You do the calculations, not with actual numbers, but with dimensions. For example, [length] + [length] = [length], [length] x [length] = [length]2, square root of [time]4 = [time]2, etc. In the final result, left and right of the equation have to be equal. For more information, search about dimensional analysis (for example, the Wikipedia article on dimensional analysis might help).
A dimensional check in an equation can provide a quick check about the possible correctness of the equation. For example, if you are supposed to calculate a speed, the dimensions of the result MUST be of the form [distance] / [time] (or something that you can simplify to distance/time). If it doesn't, the formula is wrong. If it does, it MIGHT be correct.
You need another equation to make this a linear equation so you can solve for both variables. One equation with two variables is not enough to determine the correct answer.
The least number of significant figures in any number of the problem determines the number of significant figures in the answer.
First it is necessary a correct chemical analysis of this compond, with the goal to establish the empirical chemical composition.
The correct spelling is "dimensional."
The correct set of coefficient for an equation depends with the equation in question. There are many types of equations.
to determine what problem exist and how to correct them
The correct spelling is one dimensional. A drawing on a piece of paper is one dimensional.
if an equation is given the correct answer, it is mathematically correct.
No it is not correct.