# CLASS-8INTRODUCTION OF EQUATIONS

EQUATIONS –

An algebraic equation represents the quality of two mathematical expressions involving at least one variable (literal). There are some examples are given below -

Example.1) 9 – 3x = 5             Example.2)  a² -2a = 10

Example.3)  3x + 4 = 15          Example.4)  7xᶟ + 2x² = 25x – 10

Linear Equations –

A linear equation in one variable, say ‘x’, is an equations in which the exponent of ‘x’ is 1. The general form of a linear equation is ax + b = 0. There are some examples are given below –

Example.1)  2x + 5 = 10          Example.2)  5x – 7 = 15

Example.3)   a/3 + 5 = 2a

Solution of an Equation

The solution or roots of an equation is a number, which when substituted for the variable in the equation makes the left-hand side (LHS) of the equation equal to the right-hand side (RHS). For your better understanding providing some example –

Example.1) The solution of equation a – 3 = 12 is 15 because 15 – 3 = 12

Example.2) 4 is not the solution of the equation 4x + 2 = 3x – 5 because if we substitute or replace the value of x by 4 then we find that => (4 X 4) + 2 = (3 X 4) – 5

Laws Of Equality –

Laws.1)  If the same number or quantity is added to or subtracted from both sides of an equation, the two sides remain equal. We can express this symbolically as follows –

If, x = y, then x + k = y + k and x – c = y – c

Laws.2)  If both sides of an equation are multiplied or divided by the same non-zero quantity, the sides remain equal.

If, x = y then ax = ay , where a ≠ 0

A                  B

------------ =  ----------- , where y ≠ 0

y                   y

Transposition –

Any term on one side of an equation can be shifted to the other side by changing the sign of the term. This process is called transposition.

Example.1) If w + x = y – z then w + x – y = - z or  w + x – y + z = 0

An equation remains unchanged if all the terms on the LHS are shifted to the RHS and all the terms on RHS are shifted to LHS.