How to Solve Complex Inequalities?

Any expression in which less than, greater than, less than equals to and greater than equals to (<, >, ≤, ≥) symbols are present is known as inequality. Now we will see how to solve complex inequalities. We will solve complex inequality step by step:
Steps to follow to solve complex inequality are shown below:

Step 1: Take a complex inequality. Suppose we have given a complex inequality as: 4 / 2p – 15 < 0.

Step 2: Solve the inequality for variable ‘p’. If we solve above given inequality for variable ‘p’ then we get:
2p – 15 = 0,
On further solving we get:
2p = 15,
p = 15 / 2,
p = 7.5,

Step 3: Plot the value of 'p' in graph and then check the value of 'p' for less than and greater than 7.5. Put value 6 and greater value 8 in the inequality. On putting 6 we get:
 
 
We can see in the graph:
4 / 2p – 15 < 0,
P = 6,
4 / 2 * 6 – 15 < 0,
4 / 12 – 15 < 0,
4 / -3 < 0,

On putting 'p' equals to 8, we get:
4 / 2p – 15 < 0,
P =8,
4 / 2 * 8 – 15 < 0,
4 / 16 – 15 < 0,
4 / 1 < 0.

So inequality lies in negative direction or it can also be written as: (- ∞, 7.5). In this way we can solve the complex inequality. This is all about complex inequality.