A compound inequality is a connection or relation of two or more then two inequalities joined together with "and" or "or".

In an inequality "or" indicates that as long as either inequality is true, the entire system(sentence) is true. "Or" is the combination of union of the sets the individual statements.

"And" indicates that both statements of the compound inequality are true at the same time. It is the intersection or overlap of the solution sets for the individual statements.

Like x > 5 and x < 10 is a compound inequality, which states that x takes the values greater then 5 and less than 10.

0 $\leq$ x $\leq$ 4 is again a compound inequality, where x is either 0 or 5 or any number between 0 and 5.

Solving Compound Inequality with "And" and "Or":
To solve any compound inequality, we follow some steps:
(1) First solve each inequality separately.

(2) Add or subtract the number term on each side of both terms.

(3) Multiply or divide of each side of both inequalities, by the required number. If we
multiply any inequality by a number with the negative sign then sign of inequality
will change.

(4) We just remember the thing that the word "and" indicates the overlap or
intersection is the required result and the word "or" indicates combine the
solutions i.e. find the union of the solution sets of each inequality.

(5) Draw the solution on the number line if its required.