Find the value of x

The term x is an element of alphabets. Generally, in mathematics it is used as a variable. The variable is defined as the letter which represents a number (not only the letters, can a symbol also used as a variable). The number which is represented by the variable is called the co-efficient of that variable. In algebra, polynomials are formulated from one or more variables (such as x) and also by symbols.

Procedure of Solving for X:

State all the possibilities given.
Simplify the equation.
Isolate the variable to find its exact value
Simplify the equation to get the value of the variable.

Sample Problems:

Pro 1:  Solve the following equation and find the value of x.

                     2x + 5 = 3

Sol :    Given 2x + 5 = 3

   To simplify the equation subtract 5 on both sides

       2x + 5 - 5 = 3 – 5

        2x = -2

   Simplifying this, we get

          x = 1

Pro 2:  Solve the equation |2x + 5| + 3 = 5

Sol :   The equation to solve is given by.

            |2x + 5| + 3 = 5

   Subtract 3 to both sides of the equation and simplify.

               |2x + 5| = 2

   |2x + 5| is equal to 2 if 2x + 5 = 2.

   Simplify the above equation

            2x + 5 = 2.

   Isolate x and simplify

                    x = -3/2

Pro 3:   Given the system of equations
     x + y = 0
     2x + 3y = 2.

Solve and find the values of x and y.

Sol :   Multiply the first equation by 2.

         2x + 2y = 0

          2x + 3y = 2

   Solve the above equation by changing the sign of the terms in second equation.

              2x + 2y = 0

             -2x - 3y = -2

    which gives the solution

           -y = -2

    Therefore,    y = 2

   Substitute y value in first equation

        x + y = 0

        x + 2 = 0

    Hence,   x = -2

Pro 4:  Solve the equation 8x^4 + 3x^2 + 4x - 5x^-1 + 2x^-3 for x = 2.

Sol :    Evaluate the equation by substitute the value of x

            = 8x^4 + 3x^2 + 4x - 5x^-1 + 2x^-3

            = 8(2)4 + 3(2)2 + 4(2) - 5(2)-1 + 2(2)-3    

            = 8(16) + 12 + 8 - (5/2) + (1/4)

            = 128 +12 + 8 - 2.5 + 0.025

            = 145.525

Problem 4:

Pro 1:  Solve the quadratic equation x^2 + 5x + 6 = 0

Sol :   Given x^2 + 5x + 6 = 0

    For finding the roots of the equation, factorize it using trial and error method.

            x^2 + 5x + 6 = 0

             (x + 2) (x + 3) = 0

     Therefore the roots are

              x = -2 and x = -3