Question

the graph to the right shows that the three components of love, namely passion, intimacy, and commitment, progress differently over time. passion peaks early in a relationship and then declines. by contrast, intimacy and commitment build gradually. use set - builder notation to write an inequality that expresses for which years in a relationship intimacy is greater than commitment.
the years for which intimacy is greater than commitment in a relationship is {x|□}.

Explanation:

Step1: Analyze the Graph

From the graph, we need to find the \( x \)-values (years) where the intimacy curve is above the commitment curve. By observing the intersection point (or the region), we can see that intimacy is greater than commitment when \( x < 8 \) (assuming the intersection is at \( x = 8 \) from the graph's grid and curves).

Step2: Set - Builder Notation

Set - builder notation for the set of years \( x \) where intimacy > commitment is \( \{x|x < 8\} \) (or depending on the exact intersection, but from the visual, the key inequality is based on the \( x \)-axis where the two curves cross, and before that, intimacy is above commitment).

Answer:

\( x < 8 \) (so the set - builder notation is \( \{x|x < 8\} \))