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How to Solve Complex Inequalities?

TopAny expression in which less than, greater than, less than or equal to and greater than or equal to (<, >, $\leq$, $\geq$) symbols are present is known as an inequality.
Now, we will see how to solve complex inequalities. We will solve complex inequality step by step as follows:

Steps to be followed to solve complex inequality are shown below:

Step 1: Take a complex inequality. Let us consider a complex inequality $\frac{4}{2p - 15}$ < 0.

Step 2: Solve the inequality for variable â€˜pâ€™. If we solve the above given inequality for variable â€˜pâ€™, we get
$2p - 15 = 0$
On further solving, we get
2p = 15

p = $\frac{15}{2}$

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:

$\frac{4}{2p - 15}$ < 0

P = 6

$\frac{4}{2 \times 6 - 15}$ < 0

$\frac{4}{12 - 15}$ < 0

$\frac{4}{-3}$ < 0

On putting 'p' equals to 8, we get

$\frac{4}{2p - 15}$ < 0

P = 8

$\frac{4}{2 \times 8}$ - 15 < 0

$\frac{4}{16}$ - 15 < 0

$\frac{4}{1}$ < 0.

So, inequality lies in negative direction or it can also be written as (- $\infty$, 7.5). In this way, we can solve the complex inequality.