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Q: How can you tell that an equation has the same solution as the original equation?

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A line is represented by an equation. Each solution of the equation is a point on the line, and each point on the line is a solution to the equation. So the line is just the graph of the solution set of the equation.

Substitute the coordinates of the point into the equation and if the result is a true statement then the point is a solution, and if not it isn't.

When an equation is based on false assumptions, you know that it has not solution. At other times, you may be able to tell through trying to solve the equation and constantly failing.

Depends on the type of math problem. there's usually an equation to see if there is a solution or not.

by when you cancelled the variables and the two numbers left are equal. ex.5=5, is a many solution equation, in the other hand if is like this 6=5, is a no solution.

An equation is balanced if each atom on both sides are the same amount

You can be certain if the equation is linear, that is, of the form ax + b = 0 where a and b are constants.

Difficult to tell because of problems with the browser. 4x = 2x IS a linear equation whose solution is x = 0

you can't. x=-2 if that equation is true

The exact procedure to use can only be decided after you examine the equation. Different equations are attacked in different ways. All I can tell you in general is: Whatever you do to one side of the equation, you must immediately do the same to the other side. Follow this rule enough times, and you'll eventually be looking at the equation's solution.

the number of atoms (of each element) should be the same on either side of the chemical equation.

It depends on your equation. Your equation will tell the proportionallity and then will we be able to tell what will happen to the other variables and or just one variable.

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