# Algebra

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Algebra is a branch of mathematics in which letters are used to express the numbers, dimensions of a figure or many other things. These letters are called variables.

Variable is a symbol which is used to represent unknown numbers. The value of a variable is not fixed. It can take different values. Letters n, l, m, p, x, y, z, etc. are used to show a variable.

Variables allow us to express many general rules or formulae in a concise and easy way.

Area and perimeter of geometrical figures can be expressed using variables.

Perimeter of Square = 4 x a, where a = side of the square.

Perimeter of Rectangle = 2 x (l + b), where l = length of the rectangle, b = breadth of the rectangle
The use of variables allows us to express the generality of commutative and distributive property of numbers such as
a + b = b + a (Commutativity of addition of two numbers)
a x b = b x a (Commutativity of multiplication of two numbers)
a(b + c) = ab + ac (Distributivity of multiplication over addition of numbers)
where variables a, b and c represent numbers.

Operations of addition, subtraction, multiplication and division can be done on variables.

An expression including any variable say x can be evaluated only if x is given some value. If the value of variable is given, then the value of given expression can be found.

An equation is a condition on a variable and it is written with an equal sign. An equation has two sides, LHS and RHS, between them is the equal (=) sign.

In an equation, the value of L.H.S. (Left Hand side) should always be equal to the value of R.H.S. (Right Hand Side).

A number that satisfies an equation, i.e., by substituting the number in the equation, the LHS and RHS of the equation become equal, is called the solution of that equation.

One method of obtaining the solution of an equation is trial and error method, where some values are given to the variable and it is checked whether it satisfies the equation. This process is continued until right value is obtained that satisfies the equation.

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