INEQUALITY

What is Variables?
An element, a feature, or a factor that is liable to vary or change to find any equation and represent by x, y, z etc.
Example: 3x + 27y = 40 is variable
Example: 2y + 5x = 12 is variable.

What is Constant?
A constant is special number or a real number usually or whose value is fixed in the context of use is called a constant.
Example: 5x – 3y + 2z = 24 here is 5, 3, 2, 24 are constant value.
Example: 4y + 7y – 9z = 53 here is 4, 7, 9, 53 are constant value.



6x2 +11x + 3 = 0

6x2+9x+2x+3=0
3x(2x+2)+1 (2x+3)=0
= -3 / 2  or – 1 / 3 .

Example:
4y2 + 12y + 8 = 0
Answer:
Shortcut tricks:
4  x 8 = +32
we break + 32 in two parts such that addition between them is 12.
+32 = (+8) + (+ 4) = +12 .
Change sign of both factor and divide by coefficient of y2 ,
So – 8 / 4 = – 2 .
– 4 / 4 = -1
i. e . – 2, – 1  .
Relation between two variables
x>y
x>y
x<y
x<y
x = y relation cannot be determined.
 5x2 + 11x + 6 = 0
4y2 + 10y + 6 = 0
In equation one multiply 5 and 6 get the result is 30 separate 30 as 5 and 6 which is addition of 5+6=11.
In equation one multiply 4 and 6 get the result is 24 separate 24 as 4 and 6 which is addition of 4+6=10.
and switch the sign in to negative and divide by coefficient of x2. -5 / 5 = -5 and -6 / 5 = -6 / 5.
and the second equation is do same that is -4 / 4 = -1 and -6 / 4 = -3 / 2.
Now we get the solution is for x = -5 and -6 / 5.
Now we get the solution is for y = -1 and -3 / 2.
Example:
7x + 3y = 15……. Equation 1
10x + 5y = 10……. Equation 2
Answer:
At first we multiply the equation by 5 & 3
7x + 3y = 15……. Equation 1            (Multiply by  5 )
10x + 5y = 10……. Equation 2          (Multiply by  3 )
35x + 15y = 75……. Equation 1        (Multiply by  5 )
30x + 15y = 30……. Equation 2        (Multiply by  3 )

5x = 45 .
x = 9 .
We apply value of x in any equation to obtain y value
we apply in equation 1
7 x 9 + 3y = 15
63 + 3y = 15
3y = 65 – 15
y =  17  Approx
So , x = 9 and y = 17