Question

why is it possible for a compound inequality to have a solution with only one bound? how is that bound decided?

Explanation:

Step1: Understand compound inequalities

A compound - inequality can be a conjunction (and) or a disjunction (or). When it is a disjunction of two inequalities, if one of the inequalities is always true for a certain set of values and the other has a non - overlapping part, it can result in a solution with one bound.

Step2: Analyze how the bound is decided

The bound is decided by solving the non - trivial inequality in the disjunction. For example, if we have the compound inequality $x>2$ or $x + 5>x$, the second inequality $x + 5>x$ is true for all real numbers. So the solution of the compound inequality is $x>2$, and the bound $x = 2$ comes from solving the first non - trivial inequality.

Answer:

It is possible for a compound inequality to have a solution with only one bound when it is a disjunction and one of the inequalities is always true. The bound is decided by solving the non - trivial inequality in the disjunction.