# Examples of Inequality and Compound Inequality

Example:
Solve and graph the solution of the inequality ${\text{x}} + 3 > 4{\text{x}} + 6$

Solution:
We have

Thus, the solution set is
Solution Set $= \left\{ {{\text{x:x}} \in \mathbb{R} \wedge {\text{x}} < - 1} \right\} = \left] { - \infty , - 1} \right[$

The graph of the solution set is

Example:
Solve and graph the solution of the inequality $11 - 2\left( {{\text{x}} - 1} \right) \geqslant 8 - 2\left( {{\text{x}} - 2} \right)$.

Solution:
We have

Here equality is not possible because 13 is always greater than 12, in $13 > 12$. So, the solution of the given inequality is the set of all real numbers is $\mathbb{R}$.

The solution can be written as $\left] { - \infty ,\infty } \right[$