Algebra is an extension of arithmetic. It handles unknown numbers along with known numbers. Unknown numbers are called variables. They are represented as alphabets such as a,b,x,y etc.
Mathematical statement 1 + 2 = 3 is true while 1 + 2 = 5 is false.
However, a statement like x + 1 = 3 is neither true nor false. x is a variable and may be given any value. The statement is true only for x = 2.
x + 1 = 3 is an algebra equation.
For what value of x is the equation x − 5 = 15 true?
Since 20 − 5 = 15, x must be replaced by 20 to make the given statement true.
Another way to arrive at the same result is
x − 5 = 15
x = 15 + 5
x = 20
Four more than twice a number is 16. Find the unknown number.
Let the unknown number be x . According to the given statement
2x + 4 = 16
2x = 16 − 4
2x = 12
x = 12 ⁄ 2
x = 6
6 is the required number.
Kim is 2 years younger than Ali. The sum of their ages is 20. Find their ages.
Let Ali’s age be x
Then Kim’s age is x − 2
Since the sum of their ages is 20
x + x − 2 = 20
2x − 2 = 20
2x = 20 + 2
2x = 22
x = 22 ⁄ 2
x = 11
Ali is 11 years old. So Kim who is 2 years younger is 9 years old.
The use of algebra equations to solve simple real world problems is very old.
Egyptians worked on simple real world algebra problems as early as 2000 BCE. This is because problems that need solution by algebra equations are encountered very often in practical life. Algebra equations help easy solution to many practical problems of real life.
However, the compact symbolism of algebra equations used today appeared much later. Solving equations in algebra is greatly simplified by the signs and symbols that are now used. Reconsider the solution of example 3 mentioned above. Imagine how harder it would be to mention logical steps of the solution in plain English language.
Areas of math other than algebra also enable us solve problems that we come across in our daily lives or in the pursuit of knowledge. As said by the American mathematician S. Gudder
The essence of mathematics is not to make simple things complicated, but to make complicated things simple.
To know more about algebra equations read the excellent article at the link