The solution of equations originates with ancient Egypt. Algebra facilitates the declaration of what is known about a variable or variable using something akin to a mathematical sentence as an Equation of an Inequality. These mathematical sentences allow you to perform operation on the two sides to find the value or values of the variable. Normally this involves performing one or more operations on one side of the equation to isolate the variable on one side. The other side is used to display the solution. This, the solution of equations, is the heart of Algebra.

Algebra can be used in problems involving distance, rate, time, change in property or value and change in general. It is found in economics, statistics, physics, chemistry, astronomy and astrophysics, biological sciences, and various other disciplines. It is the essential tool of mathematics marking the transistion from arithmetic to the higher forms.

A variable is a symbol for which one or more quantities may be substituted. For example, in the ALGEBRAIC EXPRESSION 4x, where

4x = x+ x + x + x

x is a variable, and it can be replaced by any real number, for example, 1, 2, 3, 1/2, -5, or 0. On the other hand, to make the algebraic expression

4y = 8

a true statement, the variable y can be replaced only by 2.

When variables represent real numbers, they can act like numbers in any arithmetic operation. Variables can be added, subtracted, multiplied, or divided (excluding division by zero). And it is possible to raise a variable to a power or to extract a root of a variable.

Algebra allows you to express what is known about some variable (or variables) in terms of mathematical sentences (an equation or an inequality) and to perform operations on the two sides of a mathematical sentence in order to find the value (or values) of the variable. Usually an equation is solved by performing one or more operations on both sides of the equation in order to isolate the variable on one side. Then the other side of the equation will give the solution

Example.

Let's solve for x in the following equation:

3x+4=19

To solve this equation, first subtract 4 from both sides,

3x+4-4=19 -4

giving

3x=15

divide both sides by 3,

3x/3=15/3

giving

x=5

Using algebra, you can solve problems that cannot easily be solved with arithmetic alone.

Example.

On the route home from a double dutch contest, the twenty participants stopped for a drink. Each of them had either a can of Coke @ $0.65 or a small carton of milk @ $0.45. The coach paid $10.75 for their drinks. How many drank Coke?

Solution: Let x represent the number who drank Coke. Then 20-x represents the number who drank milk. The cost may be represented by

0.65x + 0.40(20 - x) = 10.75

or after multiply (0.40 * 20) and (0.40 * x)

0.65x +8.00 -0.40x = 10.75

then reorganizing the equation we have

0.65x - 0.40x+8.00 = 10.75

and then

(0.65 - 0.40)x+8.00 = 10.75

If we submtract 8.00 from each side, we have

(0.65 + 0.40)x +8.00 - 8.00 = 10.75 - 8.00

or

0.25x = 2.75

which means that

x=11