components of algebra

In this article components of algebra, we will discuss algebra and the components of algebra. Algebra is a part of mathematics, which mainly deals with the expressions, variables and arithmetic operators. Algebra leads to understand the mathematical concepts from the childhood. Generally any part of the mathematical word problems is converted to algebraic equations prior since which is the easiest method to find the solution by solving the algebraic equation. Let us discuss some example for components of algebra.

Components of Algebra:

Consider the following algebraic equations given below,

`x+5(x+8)=70`

The above line is fully named as algebraic equation or algebraic expression

In the above algebraic equation,

x is variable

‘+’ algebraic operator

Numbers are the constant

Consider the following algebraic equations given below,

`x+y=15`

Algebraic Equation may contain the single variable,two variable or it may contain multivariable .Here the above equation contains the two variable.

Consider the following algebraic equations given below,

`x+sin x +e^(x)=6`

Algebraic equation may contain some other functions such as trigonometric function exponential function or logarithmic function.

Example Problem for Components of Algebra:

Example problem 1- Components of algebra

An integer is six more than another integer, sum of the twice the smallest integer and four times the greatest integer is 54. What is the greatest integer?

Solution:

Consider Smallest integer x

Greatest integer x+6

2x+4(x+6) =70

2x+4x+24=70

6x+24=54

6x=30

x=5

Smallest integer x=5

Greatest integer x+6=11

Example problem 2- Components of algebra

The ages of Paarthi and Sabari differ by 12 years when comparing. If 3 years ago, the elder one be 5 times as old as the younger boy, find Paarthi and Sabari present ages.

Solution:

Consider the age of the Paarthi be x years

The age of the Sabari = (x + 12) years

:. 5 (x - 3) = (x + 12 - 3)

5x-15=x+12-3

4x=15+12-3

4x=27-3

4x=24

x=6

Paarthi present age is 6 years

Sabari present age is 18 years