Introduction for algebra origins:

Algebra is a branch of mathematics. Algebra plays an important role in our day to day life. The word algebra is derived from Arabic word al-jabr, Which is invented by the Arabic mathematician Mohammed ibn-Musa al-Khowarizmi. The origin of algebra executes the four basic operations such as addition, subtraction, multiplication and division. The most important terms in algebra origin are variables, constant, coefficients, exponents, terms and expressions. In Algebra, besides numerals we use symbols and literals in place of unknown numbers to make a statement. Hence, Algebra origin may be regarded as an extension of Arithmetic.

 

 

Most important terms for algebra origins:

 

Variables

 Algebraic variables are the alphabetical characters which are used for assigning the value. While solving the algebraic equation value of the variable will be changed. Widely used variables are x, y, z

Constant

An algebraic constants are the value whose value never change during the solving the algebraic equation. In 2y + 5, the value 5 is the constant.

Expressions

An algebraic Expression is the combination of variables, constant, coefficients, exponents, terms which are combined by the following arithmetic operations Addition, subtraction, multiplication and division. The example of an algebraic expression is given below

                                                              2y + 5

Term

Terms of the algebraic expression is concatenated to form the algebraic expression by the arithmetic operations such as addition, subtraction, multiplication and division. In the following example 3n2 + 2n the terms 3n2, 2n are combined to form the algebraic expression 3n2 + 2n by the addition operation ( + )

Coefficient

        The coefficient of an algebraic expression is the value is present just before the terms. From the following example, 3n2 + 2n the coefficient of 3n2 is 3 and 2n is 2

 

Order of the operation for algebra origins:

 

      1. First, simplify the expression with in the parentheses.

     2.  Next, simplify  the exponents.

     3.  Next, simplify the multiplication or division operation.

     4. Finally,  simplify the addition or subtraction operation.

 

Examples for algebra origins:

 

   Example 1:

          3(a-2) + 10 = 0

      Solution:

            3(a-2) + 10 = 0        

           3a – 6 + 10 = 0

                  3a + 4 = 0

              3a + 4 - 4= 0 – 4 (Add -4 on both sides)

                        3a = -4

                   3a / 3 = -4 / 3 (both sides divided by3)

                        A = -4 /3

   Example 2:

                5x - 10 = 15x - 20  

       Solution:

                5x - 10 = 15x - 20

          5x - 10 + 10= 15x – 20 + 10    (Add 10 on both sides)

                       5x =15x -10

              5x – 15x =15x -15x  - 10 (Add  -15x on both sides)

                    -10x = -10

              -10x / 10 = -10 / 10 (both sides divided by 10)

                        -x = - 1 which is equal to x=1

   Example 3:

          10x + 20 = 30

      Solution

                10x + 20 = 30

          10x + 20 - 20 = 30 - 20 (Add -20 on both sides)

                        10x = 10

                  10x / 10 = 10 / 10 (both sides divided by 10)

                            x = 1

 

   Example 4:

        Solve the equation   |-25x + 50| -75 = -100

      Solution:

                    |-25x + 50| -75 = -100

              |-25x + 50| -75 + 75= -100 + 75(Add 75 on both sides)

                          |-25x + 50| = -25

               |-25x + 50| is same as -25x + 50, now solve for x

                             -25x + 50= -25

                             -25x + 50= -25 - 50 (add -50 on both sides)

                                    -25x=-75

                            -25x /- 25 = -75 / -25 (both sides divided by -25)

                                        x = 1