Final answer:
Inequalities are graphed on a horizontal number line using open or closed dots to indicate inclusion of the endpoint, shaded to the right for greater than and to the left for less than. The line extends indefinitely, encompassing all possible values outlined by the inequality.
Step-by-step explanation:
To understand how the numbers in the inequality would be positioned on the horizontal number line, let's consider some basic principles. When we graph inequalities on a number line, we use an open or closed dot to represent whether the number is included in the solution set (closed dot for \u003C= or \u003E=) and an open dot for \u003C or \u003E. The number line extends indefinitely to the left (towards more negative values) and to the right (towards more positive values). Inequalities dictate a span or range of values that fulfill the condition, so we shade the area of the number line where the inequality holds true.
For example, if we have the inequality x \u003E 3, we place an open dot on 3 to indicate 3 is not included and shade the number line to the right of 3, representing all values greater than 3. Conversely, if x \u003C= -2, we would place a closed dot on -2 (since -2 is included) and shade to the left, signaling all values less than or equal to -2 are solutions. Graphing such inequalities provides a visual representation of the possible values x can take.
When dealing with income inequality or concepts such as the Lorenz curve, we represent data on coordinate systems or curves. However, the question at hand specifically pertains to the simple positioning of inequality values on a horizontal number line, which is a fundamental concept in representing inequalities in algebra.