## ALGEBRA - ESSENTIAL POINTS

• The algebra is the branch of mathematics, in which the value of unknown is determined. It develops the tool for solving complex problems and puzzles.
• Algebraic expressions consist of variables and constants.
• Variable: Symbols which are used to represent or replace numbers. They are denoted as x, y, z, a, b, c…… and can take different numerical values. We generally use small letters to represent variables.
• Constant: A symbol having a fixed numerical value. Example: 2, -10, etc.
• By the help of setting of equations in algebra, the value of unknown quantity or variable is ascertained in numbers.
• The variable's value is not constant, it varies. For instance the number of sides of the triangle is fixed to three and hence it is not a variable. But the length of its sides is variable, as its length could be any.

Example 1: Write the equation for a number when divided by 4 and 5 is added to it gives 23.

Solution: Let the number be y

So y/4 + 5 = 23.

Example 2: Thirty less than twice the number gives 20.

Solution:  Let the number be y

Hence 2y – 30 = 20

2y = 20 + 30

2y = 50

Hence y = 25

• The equation 3y + 6 = 5 is similar to 6y + 12 = 10
• When we have to add variable y four times, it is y + y + y + y or 4y