how to solve inequalities with fractions

Before discuss the inequality with fraction, it is necessary to know about the inequality and fractions. So first we see the equation of inequality look like, what are the conditions of inequality.
If we have two variable y and z, then there is many more condition for the inequality equations.
Suppose y is less than equal to z;
⇒y ≤ z;
Inequality present;
y is greater than equal to z then we can write:
⇒y ≥ z;
And if y is greater than z then we can write;
⇒y > z;
And if y is smaller than z then we can write;
⇒y < z;
These all are the properties of inequality. If in any equation these symbols are present then we can say there is an inequality in the expression otherwise the expression is simple equation.
And any number which is written in the form of o/p, that type of number is known as fraction. Now we will see how to solve inequalities with fractions? To solve the inequality with fraction, we change it into an equation without fraction. By this technique we know how to solve the equation. This technique is said to be clearing.
Before solving these types of equation you have to recall all the rules for adding, subtraction, multiplying and dividing fractions.
     In these types of equations, firstly we take the constant term to one side of the equation and variables are taken on another side. And solve the equation and after solving we get the value of unknown variables.
There are some steps which explain how to solve the inequality equations with fractions:
Step1: First we will Multiply both side of the equation by both LCM of the denominator.
Step 2: Then after solving every denominator will then cancel, after this we will get the equation without Fractions.
Step3: After that we find the L.C.M. and multiply the L.C.M. on both side of the equation.
We have to follow these steps to solve the equation.
 By using above steps we will see some of the examples which are given below
Example: -    P + P – 4 ≤ 9; solve the inequality equations with fractions?
                     5     6

Solution: - By using all the above steps we can easily solve this inequality.

                       P  + P – 4   ≤ 9;
                       5         6
 The LCM of 5 and 6 is 30. Therefore multiply every term on both sides by the value 30.

       6P + 5P –20 ≤ 9;
              30
⇒6P + 5P – 20 ≤ 30 * 9;
Now we add all the like term which are present in the equation:
⇒11P – 20 ≤ 270;
On further solving this equation we get
 ⇒11p ≤ 270 + 20;
 11P ≤ 290;
 P ≤ 290/ 11;
P ≤ 26.36;
After solving the inequality we get the value of P is greater then 26.36;
Example 2: -    P   - 4P   ≥ 1; solve the equations with fractions?
                        3       2       4
 Solution: -       P - 4P   ≥ 1;
                        3      2       4
Multiply both side of the equation by both LCM of the denominator.
 After solving every denominator will then cancel, after this we will get the equation without Fractions. (Know more about inequalities in broad manner, here,)
 The LCM of 3, 2 is 6. Therefore multiply every term on both sides by the value 6.

         P – 4P ≥ 1,
         3    2      4

         2P – 12P ≥ 1;
               6          4

           -10P ≥ 6 / 4;

           -40P ≥ 6;
            P ≥ 6 / -40;
           P ≥ -0.15;
After solving the inequality equation we get the value of P is less than 0.15;
Now we see Binomial Probability Formula:
= (n) x^p y ^{n - p}
   (p)
Where n is number of trials:
p is number of successors;
n - p is number of failures;
These all are used in board of secondary education ap ,
In the next session we will discuss about Compound Inequalities and if anyone want to know about Multiplying Rational Expressions then they can refer to Internet and text books for understanding it more precisely.