well its really simple what you need to understand is the unknown and constant, unknown are letters for example (X, Y, N etc.) and the constant are the numbers. (1,2,3 etc)
well the equal to sign (=) is like a bridge both the constant and unknowns has to cross.
remember when doing inequalities you should separate the
unknowns and the constants.
well lets try it:
7x+4=3x+16
1st step: separate the unknowns and the constants
i will put all the unknowns in the left hand side and the constants on the right hand side
7x - 3x=16 - 4
VERY IMPORTANT: when both the constant and unknown crosses the ( = ) bridge, their sign either ( - or + ) changes.
what happen is that after +3x and +4 crosses the bridge it becomes -3x and -4. you should note that any number is positive (+) number
2nd step: so then it become quite simple you add the unknown and the constant in other word you simplify the equation.
7x - 3x=16 - 4
4x=12
3rd step: you should always simplify the equation in a way that the unknown stand alone ( i mean that our goal is to know the value of x) so we need to convert 4x into x.
the number which appear before the unknown is called a coefficient. example (the coefficient of 4x is 4, the coefficient of 3x is 3, the coefficient of 5x is 5, the coefficient of x is 1,)
4x=12
now we should eliminate the coefficient 4x in order to find the value of x.
the only way to eliminate coefficients is use division.
NOTE THAT when you divide an unknown you should also divide the constant which is on the other side of the (=) bridge
4x=12
in order to get x, by what factor should i divide 4x?
by 4, why?
because 4x divide by 4 makes x.
if i divide my unknown by 4 i should also divide my constant by 4.
so.........
x=3. TADA...
now 1/4(6n-3)=4n+1
when there is a number before a bracket that mean the number multiplies with the constant and unknown inside the bracket.
(6n-3) is inside the bracket, 1/4 is before the bracket.
1st step. simply the left hand side of the equation by multipling 1/4 and (6n-3)
which gives 1/4 x 6n= 6/4n
1/4 x -3= -3/4
so the left hand side of the equation becomes:
6/4n - 3/4=4n+1
by applying all the steps i teach you
6/4n - 3/4=4n+1
6/4n-4n=1+3
-5/2n=4
now you divide by -5/2
n= -8/5 voila....
ONE MORE THING I FORGET TO MENTION WHEN YOU DIVIDE A NEGATIVE UNKNOWN THE CONSTANT ALSO MUST BE DIVIDE BY THE NEGATIVE UNKNOWN.
for example:
-3x =3
x= -1
-1/2x=4
x= -8
and
-5y= -25
y= 5
well i this website
http://mathworld.wolfram.com/WolfPrize.html
i used when i was in high school
