10.1 Introduction: Equation is a mathematical statement written in symbols showing the equivalence between two things. They are written with an equal sign.
For example
3 + 5 = 8
9 – 3 = 6
10.2 Terms and Factors: the simplest of equation is
ax + b = 0 (i)
Where a and b are constants and x is a variable.
Equation Solver for ax^{2}+bx+c = 0 |
a = 1; b = 2; c = 1. The roots are degenerate: x1 = -1.00; x2 = -1.00. |
Constants: the number present in the equation is called Constant. Constants are fixed numbers and cannot be changed in a given equation. In the above equation, a and b are constants. Where a and b can be any numeral value.
Example : 3x + 7 = 0
In the given equation 3 and 7 are fixed values and are called as Constants.
Variables: A variable is a literal symbol and is so called because its value may vary.
A variable is a blank or empty symbol. And we can assign any value, whether a positive number or a negative number, a whole number or a fraction.
In equation (i) x is the variable and can be assigned any value.
Identity: An identity is an equation which is true regardless of the values of variables in it.
Example: x(x – 1) = x^{2} – x is an identity.
Because, it holds true for any value of x.
But
x^{2} – x = 0 is not an identity.
As it does not hold true for infinite values of x except the roots or the solution of the equation. That is x = 0 and x = 1.
10.5.1 Addition equation: One term in an equation is unknown and its value needs to be determined. Variable is the unknown term in the equation. These equations are solved by finding the value of variable.
Example: solve x + 5 = 10
This equation can be solved by using subtractive property.
x + 5- 5 = 10 – 5
x + 0 = 5
x = 5
10.5.2 Subtraction equation: these equations are solved by using the additive property.
Example: solve x - 4 = 16
x - 4 = 16
x – 4 +4 = 16+4
x = 20
10.5.3 Multiplication equation: These equations are solved by using the division property.
Example: solve x = 5
x x 10 = 50
x x 10/10= 50/10
x = 5
10.5.4 Division Equation: these equations are solved by using the multiplication property.
Example: solve x / 3= 5
x/3 = 5
(x /3) x 3 = 5 x 3
x = 15
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