Simplifying Algebra Equation

Introduction to simplifying algebra equation:

        An algebra equation is a mathematical statement that asserts the equality of two expressions. An algebra equations consist of the expressions that are to be equal on opposite sides of an equal sign, as in

                x+3=5

        One use of an algebra equations is in mathematical identities, assertions that are true independent of the values of any variables contained within them. For example, for any given value of x it is true that

                x(x-1)=x^2-x

         However, an algebra equations can also be correct for certain values of the variables.

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Problems on Simplifying Algebra Equation:
 Solve equation of the form ax+b=c

              In solve equation of the form ax+b=c, the goal is to rewrite the equation in the form variable=constant. This needs applying both the addition and the multiplication property of equations.

           Solve:`(2)/(5)` x-3=7

  Solution:

                        `(2)/(5)` x-3=-7

                        `(2)/(5)` x-3+3=-7+3       add 3 to each side of the equation.

                        `(2)/(5)`x=-4                  Simplify.

                        `(5)/(2)`*`(2)/(5)`x=`(5)/(2)`(-4)            Multiply each side of the equation by the coefficient 5/2

                        x=-10                    Simplify. Now the equation is in the form variable=constant.

Example 2:

Solve: 3x-7=-5

Solution:

            3x-7=-5

            3x-7+7=-5+7                      Add 7 to each side of the equation.

            3x=2                                 Simplify.

            `(3x)/(3)` =`(2)/(3)`                               Divide each side of the equation by 3.

            x=`(2)/(3)`                                 Simplify. Now the equation is in the form variable=constant.

            The solution is `(2)/(3)`.            Write the solution.



Example 3:

            Solve: `(1)/(2)`=x+`(2)/(3)`

Solution:

            `(1)/(2)`=x+`(2)/(3)`

            6(`(1)/(2)` )=6(x+`(2)/(3)`)           Multiply both side of the equation by 6, the LCM of the denominators.

            3=6(x)+6(`(2)/(3)`)           Simplifying equation. Use the Distributive Property on the right side of the equation.

            3=6x+4                 Note that multiplying both side of the equation by the LCM of the denominators eliminated by the fractions.

            3-4=6x+4-4             Add -4 to each side of the equation.

            -1=6x                     Divide each side of the equation by 6.

            x=-`(1)/(6)`                       Simplify. Now the equation is in the form variable=constant.

Practices Problems on Simplifying Algebra Equation:
Problem 1                  

           Solve: 4x-1=5

           Answer: x=1

Problem 2:

            Solve:  `(1)/(2)`=x+`(1)/(3)`

             Answer: -`(1)/(2)`