Algebra

            Algebra is a branch of mathematics that can be characterized as a generalization of arithmetic. Algebra came from the Arabic word “al-jabr” which means “meeting”, “relationship”, or “completion”. Algebra is also the name of an abstract algebraic structure, namely the algebra in a field. Inventor of algebra is Abu Abdullah Muhammad Ibn Musa Al-Khawarizmi.

The Types of Algebra

            Algebra can be divided into the following categories:

·         Basic algebra, which note the operating properties of real numbers, using the symbol as a “substitute” to denote constants and variables, and learn the rules of mathematical expressions and equations involving these symbols.

·         Abstract algebra, which is axiomatic define and investigate algebra structures such as groups of mathematics, rings of mathematics and fields of mathematics.

·         Linear algebra, which is studying the specific properties of the vector space (including matrix)

·         Universal algebra, which studies the properties owned all algebraic structures

·         Computer algebra, which collects symbolic manipulation of mathematical objects

The Form of Algebra

            Forms such as 2a, -5b, x³, 3p + 2q called algebraic form. In algebraic form 2a, 2 is called the coefficient, while a is called variable.

Linear Equations and Linear Inequations

·        One Variable Linear Equations

Linear equations of one variable means a cubic equation. In this linear equation applies to the law: hamster eating hamster. Left-hand side and the right side can be multiplied or divided by the same number.

Example :

1.    R + 3 = 10

     R + 3 -3 = 10 – 3 (equally reduced by the same number is 3)

     R = 7

2.    3p = 12

3p / 3 = 12 / 3 (equally divided by the same number is 3)

p = 4

·         One Variable Linear Inequality

One variable linear inequality means open sentense that has the sign <, >, In linear equations applies to the law:

1.      Left and right sides can be added, reduced, multiplied, or divided by the same number.

2.      If the variable has minus sign, it should be changes to positive by multiplying a negative number and reverse the sign.

Example :

1.      5v – 7 > 23

5v – 7 + 7 > 23 + 7 (equally added by the same number is 7)

5v / 5 > 30 / 5 (equally divided by the same number is 5)

v > 6

2.      -2a < 10

-2a / -2 > 10 / -2 (equally divided by the same number is -2)

a > -5