Variable and Unknown in Algebra

What is Variable and Unknown in Algebra

VARIABLE:

A symbol, usually a letter, that can represent ANY one value of a set of values is called a variable.

Usually, small letters are used to represent a variable,

like a, b, ... , s, t, ...x, y .....

For example,

In 5x, there is one variable x.

In 7ab, there are two variables a and b.

If 3n + 2 is the expression of nth term of a sequence, then n is a variable because n can be ANY one of the natural numbers.

For n = 1, First term of sequence = 3(1) + 2 = 5

For n = 2, Second term of sequence = 3(2) + 2 = 8

For n = 3, Third term of sequence = 3(3) + 2 = 11

and so on.

Remember:

A variable in an expression can only hold ONE value at a time. As shown in the preceding example, to find the first term of a sequence, n is set to 1, for the second term to be 2,...

A variable always represents a NUMBER, not any object or anything else. It depends on the situation as to which type of number it is representing: a natural number, an integer, or anyone else.

UNKNOWN:

Unknown is a variable for which the value is yet to be found. We do not know it.

For example,

Consider an equation,

5x + 4 = 14

Here, variable x is an unknown because we do not know its value and it is yet to be found. Also, there is just ONE value of x for which the given equation is true.

Do you know what is the value of x?

Yes, its 2.

So, only if x = 2

5 x + 4 become 5 (2) + 4 which gives 14

A value of unknown for which the equation is true is called a solution or root of the equation.

Thus, in above example x = 2 is the solution or root of the given equation.

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