Constants and variables

Linear equations in one variable of Class 8

CONSTANTS AND VARIABLES:

A CONSTANT is a quantity whose value remains the same throughout a particular problem.

A VARIABLE is a quantity whose value is free to vary.

e.g.

Question 1. x + 1 = 2 and

Question 2. 2y + 3 = 5

Solution: In 1 above, x + 1 is an algebraic expression in the variable x. we read it as “ x plus 1 is equal to 2”. x is some number, called variable.

Solution: In 2 above, 2y + 3 is an algebraic expression in the variable y, we read it as “ 2 times y or 2y plus 3 is equal to 5”. y is some number, called variable.

There are two kinds of constants-fixed and arbitrary. Numbers such as 7, -3, 1/2, and p are examples of FIXED constants. Their values never change. In 5x + 7 = 0, the numbers 0, 5, and 7, are fixed constants.

ARBITRARY

constants can be assigned different values for different problems. Arbitrary constants are indicated by letters-quite often letters at the beginning of the alphabet such as a, b, c, and d.

A variable may have one value or it may have many values in a discussion. The letters at the end of the alphabet, such as x, y, z are usually are used to represent variables. In 5x + 7, the letter x is the variable.

If x = 1, then 5x + 7 = 5 + 7 = 12

If x = 2, then 5x + 7 = 5(2) + 7 = 10 + 7 = 17

and so on for as many values of x as we desire to select.

If the expression 5x + 7 is set equal to some particular number, say -23, then the resulting equality

5x + 7 = -23

holds true for just one value of x. The value is -6, since

5(-6) + 7 = -23

In an algebraic expression, terms that contain a variable are called VARIABLE TERMS. Terms that do not contain a variable are CONSTANT TERMS. The expression 5x + 7 contains one variable term and one constant term. The variable term is 5x, while 7 is the constant term. In ax + b, ax is the variable term and b is the constant term.

A variable term often is designated by naming the variable it contains. In 5x + 7, 5x is the x-term. In ax + by, ax is the x-term, while by is the y-term.

question 1. What is Solving a Linear Equation?

Solution: Solving an equation means to find a value of the variable which satisfies the equation.

question 2. How do we solve the equation?

Solution: Stepwise RULES FOR SOLVING AN EQUATION

Same quantity can be added to both sides of an equation without changing the equality;
Same quantity can be subtracted from both sides of an equation without changing the equality;
Both sides of an equation may be multiplied by a same non-zero number without changing the equality;
Both sides of an equation may be divided by a same non-zero number without changing the equality.