Understanding Algebra

algebra is the branch of mathematics concerning the study of the rules of operations and relations, and the constructions and concepts arising from them, including polynomials,equations and algebraic structures.Together with geometry, analysis, topology,combinatorics, and number theory, algebra is one of the main branches of pure mathematics.
understanding algebra is easy example . The letter x is populer, but it is a good to change into different variables. if the way to understanding the algebra is can be easy to combine with the other number. for example, if jim is two years older than John is,might let x stand for john's age and (x+ 2) stand for jim's age.this is table for anderstand algebra easily

Subtraction	minus	“a number minus 2”	x – 2
	difference between	“the difference between a number and 8”	x – 8
	from	“2 from a number”	n – 2
	less	“a number less 3”	n – 3
	less than	“3 less than a number”	y – 3
	fewer than	“2 fewer than a number”	y – 2
	decreased by	“a number decreased by 2”	x – 2
	take away	“a number take away 2”	x – 2
Addition	plus	“a number plus 2”	x + 2
	and	“3 and a number”	3 + n
	added to	“8 added to a number”	x + 8
	greater than	“3 greater than a number”	n + 3
	more than	“3 more than a number”	y + 3
	increased by	“a number increased by 2”	y + 2
	total	“the total length”	l1 + l2
	sum of	“The sum of length and width”	l + w
Multiplication	times	“5 times a number”	5n
	product	“The product of 3 and a number”	3y
	at	“3 at 1.59”	3 ´ 1.59
	double, triple, etc.	“double a number”	2x
	twice	“twice a number”	2y
	of (fractions of)	“three-fourths of a number”
Division	quotient of	“The quotient of 5 and a number”
	Half of	“half of a number”
	goes into	“a numbergoes into 6 twice”
	per	“The price is $8 per 50”
Equals	Is, is the same as, gives, will be, was, is equivalent to

This table can make easily to understand the algebra , see the example below

Number/Geometry Problems

Example: Find a number such that 5 more than one-half the number is three times the number.

Let x be the unknown number.
Translating into math:	5 + x/2 = 3x
Solving: (First multiply by 2 to clear the fraction)	5 + x/2 = 3x 10 + x = 6x 10 = 5x x = 2

and other example

Example: If the perimeter of a rectangle is 10 inches, and one side is one inch longer than the other, how long are the sides?

Let one side be x and the other side be x + 1.

Then the given condition may be expressed as

x + x + (x + 1) + (x + 1) = 10

Solving:

4x + 2 = 10
4x = 8
x = 2

so the sides have length 2 and 3.