Final answer:
The question pertains to inequalities and their graphical representation. Both x > a and x < b represent ranges of values without slopes, thus none of the provided options (A, B, C, or D) are correct as they incorrectly mention slopes.
Correct option is (C)Similar: Both have positive slopes. Different: Domain of x-values.
Step-by-step explanation:
When considering the inequality graphs for x > a and x < b when a < b, it is important to understand the appearance of a positive slope and a negative slope on a linear graph. A graph where x is greater than a would essentially highlight all the x-values to the right of point a on the number line. In contrast, a graph where x is less than b would highlight all the x-values to the left of point b on the number line. Both of these graphs do not have a slope since they represent inequalities, not linear equations.
However, drawing parallels to linear functions can help illustrate the concept. A positive slope means that as x increases, y also increases, resulting in a line that slopes upwards to the right. A negative slope means that as x increases, y decreases, resulting in a line that slopes downwards to the right. In the case of the inequalities mentioned, no lines are drawn; instead, there are rays extending indefinitely to the left or right from the points a and b, depending on the inequality.
The correct answer to the question is none of the provided options (A, B, C, or D). This is because they all incorrectly refer to slopes, which are not applicable to the inequality graphs mentioned. Instead, the similarity is that both graphs designate a range of x-values that satisfy the inequality, and the primary difference is where this range is located on the number line.