Inequality and Compound Inequality

Inequality:
An inequality expresses the relative order of two mathematical expressions. The symbols $<$(less than), $\leqslant$(less than or equal to), $>$(greater than), $\geqslant$(greater than or equal to) are used to write inequalities.
Note:
The sign of an inequality is unchanged if it is multiplied or divided by a positive number,
For example,

Similarly,

Note:
The order of an inequality is reserved if it is multiplied or divided by a. negative number.
For example,

Similarly,

Linear Inequalities in One Variable:
Inequalities of the form ${\text{ax}} + {\text{b}} < 0$, ${\text{ax}} + {\text{b}} \leqslant 0$, ${\text{ax}} + {\text{b}} > 0$, ${\text{ax}} + {\text{b}} \geqslant 0$, where ${\text{a}} \ne 0$, b are constant, are called the linear equalities in one variable or first degree inequalities in one variable.
For example,

are all linear inequalities.

Compound Inequality:
A compound inequality is formed by joining two inequalities with a connective word such as “and” or “or”.
For example,${\text{x}} < 2$ and $3{\text{x}} - 2 > - 8$ is a compound inequality.

Note:
The real numbers ‘x’ which satisfy the linear inequality in one variable ‘x’ from its solution.
For example,
The solution of inequality ${\text{x}} > 3$
The graph of the solution of this inequality is given below.

The hole marked on 3 indicates that 3 is not included in the solution.
Now, the solution of inequality${\text{x}} \geqslant 3$ included 3
The graph of the solution of this inequality is given below.

The dark hole is marked on 3 indicating that 3 is included in the solution of equality.