LEARN MATH STEP BY STEP THROUGH VERY EASY PROCESS

INTRODUCTION 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.**