Final answer:
Compound inequalities with "and" are graphed as a continuous segment on a number line, where both conditions are met, while those with "or" are graphed as separate segments where at least one condition is met. Both use number lines and circles to denote inclusive or exclusive solutions but differ in the continuity of their solution ranges.
Step-by-step explanation:
When we compare the graph of a compound inequality involving "and" with that of "or," there are some notable differences and similarities. For compound inequalities involving "and," the graph is typically a single continuous segment that represents all values satisfying both inequalities. In contrast, the graph for "or" inequalities often consists of two separate segments, with each segment representing the values that satisfy one of the inequalities. However, a similarity is that both types of graphs utilize number lines to display the range of solutions and can share inclusive or exclusive end points, indicated by closed or open circles, respectively. Similarities include the use of number lines and the representation of solutions with circles (closed for inclusive, open for exclusive). Differences include that "and" inequalities will show a single, connected range of values where both conditions are true, while "or" inequalities may have two or more ranges of values where at least one condition is true. Overall, while there are some common elements in how these graphs are constructed, the graphical representation of compound inequalities with "and" versus "or" can lead to quite different appearances. The distinction lies primarily in whether a single continuous section of the number line is highlighted ("and") versus potentially disjoint sections ("or").