How to solve a Algebraic Equation

Topic: Algebraic Equation

An algebraic equation over the rationals can always be converted to an equivalent one in which the coefficients are integers (where equivalence refers to the fact that the two equations will have the same solutions). For example, multiplying through by 42 = 2·3·7, the algebraic equation above becomes the algebraic expression.

For example:

Question:

Find x for the following sum given below

1.) 5 + 2x = 10 - 3x

Answer:

5 + 2x = 10 - 3x

  + 3x    + 3x
______   ______

5 + 5x = 10

-5       -5
______    _______

 5x/5  =  5/5

     x = 1 

Question:

Find X for the following sum given below

2.) 3(2x -5) = 10 (2x - 1)

Answer:

3(2x -5) = 10 (2x - 1)

 6x - 15 = 20x -10

     +15 = +15
   _____   ______

      6x = 20x + 5

    -20x = -20x
   _____   _______

-14x / -14 = 5 / 14


       x = -5 / 14

For more help on this. You can reply me. 

Question to Find Equation of Line Passing through a Point

Topic : Equation of Line

Question : Find the equation of line passing through points (0,-1) given perpendicular to the line x + 3y = 4.

Solution :
An equation of the line through the point (0,-1) is perpendicular to the line x + 3y = 4, So
the slopes of the two perpendicular lines follow the relation m1 * m2 = -1
where m1 and m2 are the slopes of lines
m1 = - 1/3 (slope of x + 3y = 4)
m2 = ?
m1 * m2 = -1
-1/3 *m2 = -1
m2 = 3
So the required line will be having slope 3
(y - y1) = m (x - x1)
(y+1) = 3(x-0)
y + 1 = 3x
3x - y = 1