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Question 178: solve the following x+2/4=x-2/2
Answer by KMST(5484)   (Show Source):
You can put this solution on YOUR website! I suspect you meant  . That is an equation.
The equal sign says the each of the expressions on one side of the equal sign have the same value as the other
for exactly all values of  that are solutions of the equation.
If we multiply each side times  , the resulting products will also be equal to each other
for all values of that were solutions of the original equation.
Same thing goes for dividing by , which is multiplying times  .
Multiplying both sides of the equal sign times a number that is not zero,
turns one equation into an equivalent equation. They both have exactly the same solutions.
so, multiplying times 4, we get the equivalent equation  ,
which simplifies to  and then to  ,
which is equivalent to the original equation, and looks a lot easier.
Then if we add  to both sides of the equal sign,
we get  , which simplifies to  ,
another equation equivalent to the original equation,
because adding the same number or expression to both sides of an equation
gives an equation still true for exactly all values of that were solutions of the original equation.
or  is also equivalent to the original equation.
The only solution of and the original equation is  ,
because adding  to both sides of gives you equation ,
which is equivalent to and to the original equation, and is the solution.
IMPORTANT NOTE:
What you wrote is  , which simplifies to  and has no solution.
I suspect you meant .
The horizontal line with  above and below
means that what is above the line, and what is below the line must be calculated first.
The same happens for every other long horizontal line.
It is understood when you write with paper and pencil.
If you are typing, some parentheses are needed.
You must type that as  as (x+2)/4, and  as (x-2)/2 .
If you type 1000+1/1000-1 into most calculators, the calculator will add 1000 to 1/1000=0.001 to get 1000.001,
and then subtract 1 to get 999.001.
If you meant  ,
you should type it as (1000+1)/(1000-1),
with parentheses indicating that 1000+1 and 1000-1 must be calculated first,
before dividing one result by the other.
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